Edit Profile (opens in new tab) Machado, José António Tenreiro (b. 1957 d. 2021) Co-Author Distance Author ID: machado.jose-antonio-tenreiro Published as: Machado, J. A. Tenreiro; Tenreiro Machado, J. A.; Machado, J. Tenreiro; Tenreiro Machado, J.; Machado, J. A. T.; Tenreiro Machado, José António; Machado, José A. Tenreiro; Machado, José António Tenreiro; Tenreiro Machado, José; Tenreiro Machado, José A.; Machado, José Tenreiro; Machado, Jose Antonio Tenreiro; Tenreiro-Machado, J. A.; Machado, José A. more...less Homepage: http://ave.dee.isep.ipp.pt/~jtm/ External Links: ORCID · Wikidata · Google Scholar · dblp · GND · IdRef Documents Indexed: 292 Publications since 1989, including 3 Books and 3 Additional arXiv Preprints 29 Contributions as Editor · 2 Further Contributions Biographic References: 1 Publication Co-Authors: 203 Co-Authors with 284 Joint Publications 7,251 Co-Co-Authors all top 5 Co-Authors 36 single-authored 37 Lopes, António M. 27 Băleanu, Dumitru I. 17 Barbosa, Ramiro S. 16 Alfi, Alireza 15 Yang, Xiao-Jun 14 Moghaddam, Behrouz Parsa 13 Jesus, Isabel S. 12 Ortigueira, Manuel D. 10 Galhano, Alexandra M. S. F. 10 Silva, Manuel F. 9 Duarte, Fernando B. M. 9 Hassani, Hossein 9 Kiryakova, Virginia S. 8 Avazzadeh, Zakieh 8 Nikan, Omid 7 Bhrawy, Ali Hassan 7 Chen, Liping 7 de Moura Oliveira, Paulo B. 7 Pahnehkolaei, Seyed Mehdi Abedi 7 Sayevand, Khosro 7 Wu, Ranchao 6 Balachandran, Balakumar 6 Lacarbonara, Walter 6 Stépán, Gábor 6 Zaky, Mahmoud A. 5 Aghayan, Zahra Sadat 5 Costa, António C. 5 Figueiredo, Lino B. 5 Luo, Albert C. J. 5 Mainardi, Francesco 5 Naraghirad, Eskandar 5 Valério, Duarte 4 Alaviyan Shahri, Esmat Sadat 4 Boaventura-Cunha, José 4 da Graça Marcos, Maria 4 Ebaid, Abdelhalim 4 Ezz-Eldien, Samer S. 4 Lima, Miguel F. M. 4 Pinto, Carla M. A. 4 Quelhas, Maria Dulce 4 Taş, Kenan 4 Trujillo, Juan J. 3 Aljohani, Abdulrahman F. 3 Argyros, Ioannis Konstantinos 3 Behl, Ramandeep 3 Cao Labora, Daniel 3 David, Sergio Adriani 3 de Oliveira, Edmundo Capelas 3 Doha, Eid H. 3 Drăgănescu, Gheorghe 3 Fonseca Ferreira, Nuno Miguel 3 Golbabai, Ahmad 3 Ionescu, Clara Mihaela 3 Leamy, Michael J. 3 Milici, Constantin 3 Monteiro Duarte, Gonçalo 3 Mostaghim, Zeinab Salamat 3 Reis, Cecília M. 3 Rivero, Margarita 3 Rosário, João Maurıcio 3 Srivastava, Hari Mohan 3 Tar, József K. 3 Tobón, Catalina 3 Ugarte, Juan P. 2 Abdelhakim, Ahmed A. 2 Abdelkawy, Mohamed A. 2 Aldraiweesh, Ahmed A. 2 Alshomrani, Ali Saleh 2 Babaei, Afshin 2 Cattani, Carlo 2 Chaudhary, Naveed Ishtiaq 2 Chen, Wen 2 Copot, Dana 2 De Keyser, Robin 2 Fečkan, Michal 2 Fedula, Mykola 2 Ferreira, Isabel M. 2 Ferreira, José Rui 2 Gaber, Ahmed A. 2 Gao, Feng 2 Inacio, C. M. C. jun. 2 Liu, Fawang 2 Luchko, Yuri 2 Marcos, Maria G. 2 Martynyuk, Valeriy 2 Mehdipour, S. Hamid 2 Nigmatullin, Raoul R. 2 Özdemir, Necati 2 Pan, Wei 2 Pires, E. J. Solteiro 2 Quintino, D. D. 2 Raja, Muhammad Asif Zahoor 2 Volchenkov, Dimitri Yu. 2 Wang, Yushun 2 Zhou, Yong 1 Abd-Elhameed, Waleed Mohamed 1 Afraimovich, Valentin S. 1 Agarwal, Praveen 1 Agrawal, Om Prakash 1 Al-Mekhlafi, Seham Mahyoub ...and 106 more Co-Authors all top 5 Serials 44 Communications in Nonlinear Science and Numerical Simulation 29 Nonlinear Dynamics 26 Fractional Calculus & Applied Analysis 17 Applied Mathematical Modelling 13 Computers & Mathematics with Applications 12 Journal of Vibration and Control 11 Mathematical Problems in Engineering 9 Computational and Applied Mathematics 9 Abstract and Applied Analysis 8 Systems Analysis, Modelling Simulation 8 Nonlinear Systems and Complexity 7 Signal Processing 7 International Journal of Nonlinear Sciences and Numerical Simulation 6 Mathematical Methods in the Applied Sciences 6 Chaos, Solitons and Fractals 5 Applied Mathematics and Computation 4 Journal of Computational Physics 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 3 Neural Networks 3 Asian Journal of Control 3 NODYCON Conference Proceedings Series 2 International Journal of Control 2 Journal of Optimization Theory and Applications 2 Journal of Scientific Computing 2 Chaos 2 Fundamenta Informaticae 2 Entropy 2 Advances in Difference Equations 2 Advances in Mathematical Physics 2 Symmetry 2 Nonlinear Physical Science 1 Journal of the Franklin Institute 1 Physica A 1 Mathematics and Computers in Simulation 1 Optimal Control Applications & Methods 1 Stochastic Analysis and Applications 1 Optimization 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Journal of Robotic Systems 1 Numerical Algorithms 1 International Journal of Robust and Nonlinear Control 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Engineering Analysis with Boundary Elements 1 Nonlinear Studies 1 Discrete Dynamics in Nature and Society 1 Analysis (München) 1 International Journal of Applied Mathematics 1 Nonlinear Analysis. Real World Applications 1 International Journal of Pure and Applied Mathematics 1 Hacettepe Journal of Mathematics and Statistics 1 Fixed Point Theory and Applications 1 Journal of Statistical Mechanics: Theory and Experiment 1 Boundary Value Problems 1 Stochastics 1 Acta Mechanica Sinica 1 Journal of Nonlinear Science and Applications 1 Springer Proceedings in Mathematics & Statistics 1 Journal of Applied Nonlinear Dynamics 1 The Scientific World Journal. Probability and Statistics 1 Computational Methods for Differential Equations 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 IET Control Engineering Series 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Advances in Continuous and Discrete Models all top 5 Fields 122 Real functions (26-XX) 81 Ordinary differential equations (34-XX) 72 Systems theory; control (93-XX) 63 Numerical analysis (65-XX) 51 Partial differential equations (35-XX) 39 Biology and other natural sciences (92-XX) 33 Mechanics of particles and systems (70-XX) 31 General and overarching topics; collections (00-XX) 25 Dynamical systems and ergodic theory (37-XX) 22 Information and communication theory, circuits (94-XX) 18 Operations research, mathematical programming (90-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Probability theory and stochastic processes (60-XX) 16 Computer science (68-XX) 15 Statistics (62-XX) 15 Mechanics of deformable solids (74-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 11 Special functions (33-XX) 11 Optics, electromagnetic theory (78-XX) 9 History and biography (01-XX) 8 Measure and integration (28-XX) 8 Fluid mechanics (76-XX) 7 Operator theory (47-XX) 7 Statistical mechanics, structure of matter (82-XX) 7 Geophysics (86-XX) 5 Approximations and expansions (41-XX) 4 Number theory (11-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral equations (45-XX) 3 Combinatorics (05-XX) 3 Integral transforms, operational calculus (44-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Astronomy and astrophysics (85-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Quantum theory (81-XX) 1 Topological groups, Lie groups (22-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 268 Publications have been cited 5,685 times in 3,851 Documents Cited by ▼ Year ▼ Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Zbl 1116.00014 860 2007 Recent history of fractional calculus. Zbl 1221.26002 Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco 473 2011 New trends in nanotechnology and fractional calculus applications. Selected papers based on the presentations at the workshop new trends in science and technology (NTST 08), and the workshop fractional differentiation and its applications (FDA 09), Ankara, Türkei, November 2008. Zbl 1196.65021 177 2010 What is a fractional derivative? Zbl 1349.26016 Ortigueira, Manuel D.; Tenreiro Machado, J. A. 118 2015 The role of fractional calculus in modeling biological phenomena: a review. Zbl 1467.92050 Ionescu, Claramihaela; Lopes, A.; Copot, Dana; Machado, J. A. T.; Bates, Jason H. T. 117 2017 Analysis and design of fractional-order digital control systems. Zbl 0875.93154 Machado, J. A. Tenreiro 116 1997 A review of definitions for fractional derivatives and integral. Zbl 1407.26013 de Oliveira, Edmundo Capelas; Tenreiro Machado, José António 111 2014 Fractional dynamics and control. Papers based on the presentations at the 3rd conference on nonlinear science and complexity (NSC) Ankara, Turkey, July 27–31, 2010. Zbl 1231.93003 86 2012 A review of definitions of fractional derivatives and other operators. Zbl 1452.26008 Sales Teodoro, G.; Tenreiro Machado, J. A.; de Oliveira, E. Capelas 86 2019 Some applications of fractional calculus in engineering. Zbl 1191.26004 Tenreiro Machado, J. A.; Silva, Manuel F.; Barbosa, Ramiro S.; Jesus, Isabel S.; Reis, Cecília M.; Marcos, Maria G.; Galhano, Alexandra F. 83 2010 A new fractional operator of variable order: application in the description of anomalous diffusion. Zbl 1495.35204 Yang, Xiao-Jun; Machado, J. A. Tenreiro 83 2017 On exact traveling-wave solutions for local fractional Korteweg-de Vries equation. Zbl 1378.35329 Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo 79 2016 A review of operational matrices and spectral techniques for fractional calculus. Zbl 1348.65106 Bhrawy, Ali H.; Taha, Taha M.; Tenreiro Machado, José A. 78 2015 Discrete-time fractional-order controllers. Zbl 1111.93307 Machado, J. A. Tenreiro 70 2001 Fractional control of heat diffusion systems. Zbl 1210.80008 Jesus, Isabel S.; Tenreiro Machado, J. A. 67 2008 On the formulation and numerical simulation of distributed-order fractional optimal control problems. Zbl 1510.49018 Zaky, M. A.; Tenreiro Machado, J. A. 59 2017 Tuning of PID controllers based on Bode’s ideal transfer function. Zbl 1134.93334 Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Ferreira, Isabel M. 53 2004 Some pioneers of the applications of fractional calculus. Zbl 1305.26008 Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia 53 2014 Optimal variable-order fractional PID controllers for dynamical systems. Zbl 1392.49033 Dabiri, A.; Moghaddam, B. P.; Machado, J. A. Tenreiro 52 2018 Historical survey: the chronicles of fractional calculus. Zbl 1364.26002 Machado, J. A. Tenreiro; Kiryakova, Virginia 50 2017 A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010 Machado, J. A. Tenreiro 49 2003 Analysis of the van der Pol oscillator containing derivatives of fractional order. Zbl 1158.70009 Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Vinagre, B. M.; Calderón, A. J. 48 2007 A new fractal nonlinear Burgers’ equation arising in the acoustic signals propagation. Zbl 1435.35412 Yang, Xiao-Jun; Machado, J. A. Tenreiro 47 2019 A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach. Zbl 1410.65415 Yang, Xiao-Jun; Tenreiro Machado, J. A.; Srivastava, H. M. 45 2016 Extended algorithms for approximating variable order fractional derivatives with applications. Zbl 1370.26017 Moghaddam, Behrouz Parsa; Tenreiro Machado, José António 45 2017 A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels. Zbl 1376.65159 Parsa Moghaddam, Behrouz; Tenreiro Machado, José António 45 2017 A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations. Zbl 1412.65084 Moghaddam, B. P.; Machado, J. A. T. 42 2017 And I say to myself: “What a fractional world!”. Zbl 1273.37002 Tenreiro Machado, J. A. 42 2011 Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions. Zbl 1285.93024 Machado, José A.; Ravichandran, Chokkalingam; Rivero, Margarita; Trujillo, Juan J. 41 2013 Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport. Zbl 1471.65162 Nikan, O.; Avazzadeh, Z.; Machado, J. A. Tenreiro 40 2021 Fractional order calculus: basic concepts and engineering applications. Zbl 1190.26002 Gutiérrez, Ricardo Enrique; Rosário, João Maurício; Tenreiro Machado, José 38 2010 Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators. Zbl 1027.70011 Duarte, Fernando B. M.; Machado, J. A. Tenreiro 37 2002 An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index. Zbl 1341.49037 Bhrawy, A. H.; Doha, E. H.; Machado, J. A. Tenreiro; Ezz-Eldien, S. S. 37 2015 An integro quadratic spline approach for a class of variable-order fractional initial value problems. Zbl 1422.65131 Moghaddam, B. P.; Machado, J. A. T.; Behforooz, H. 36 2017 Stability of fractional order systems. Zbl 1296.93172 Rivero, Margarita; Rogosin, Sergei V.; Machado, José A. Tenreiro; Trujillo, Juan J. 36 2013 A poster about the recent history of fractional calculus. Zbl 1221.26013 Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 36 2010 A spectral framework for fractional variational problems based on fractional Jacobi functions. Zbl 06902342 Zaky, M. A.; Doha, E. H.; Tenreiro Machado, J. A. 35 2018 Stability and synchronization of fractional-order memristive neural networks with multiple delays. Zbl 1437.93098 Chen, Liping; Cao, Jinde; Wu, Ranchao; Machado, J. A. Tenreiro; Lopes, António M.; Yang, Hejun 35 2017 A new family of the local fractional PDEs. Zbl 1386.35461 Yang, Xiao-Jun; Machado, J. A. Tenreiro; Nieto, Juan J. 34 2017 Efficient Legendre spectral tau algorithm for solving the two-sided space-time Caputo fractional advection-dispersion equation. Zbl 1365.35201 Bhrawy, A. H.; Zaky, M. A.; Tenreiro Machado, J. A. 34 2016 Science metrics on fractional calculus development since 1966. Zbl 1312.26004 Machado, J. Tenreiro; Galhano, Alexandra M.; Trujillo, Juan J. 34 2013 A poster about the old history of fractional calculus. Zbl 1222.26015 Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 34 2010 Development of fractional order capacitors based on electrolyte processes. Zbl 1173.78313 Jesus, Isabel S.; Tenreiro Machado, J. A. 33 2009 Numerical solution of the two-sided space-time fractional telegraph equation via Chebyshev tau approximation. Zbl 1471.65157 Bhrawy, Ali H.; Zaky, Mahmoud A.; Machado, José A. Tenreiro 32 2017 Fractional electrical impedances in botanical elements. Zbl 1229.78023 Jesus, Isabel S.; Tenreiro Machado, J. A.; Cunha, J. Boaventure 32 2008 Entropy analysis of integer and fractional dynamical systems. Zbl 1211.37057 Tenreiro Machado, J. A. 32 2010 Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. Zbl 1354.35180 Yang, Xiao-Jun; Machado, J. A. Tenreiro; Hristov, Jordan 30 2016 Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011 Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia 30 2015 SM-algorithms for approximating the variable-order fractional derivative of high order. Zbl 1377.65031 Moghaddam, B. P.; Machado, J. A. T. 29 2017 Introduction to fractional differential equations. Zbl 1417.34004 Milici, Constantin; Drăgănescu, Gheorghe; Machado, José António Tenreiro 29 2019 Fractional-order control of a hexapod robot. Zbl 1096.70004 Silva, Manuel F.; Machado, J. A. T.; Lopes, A. M. 29 2004 Editorial: Fractional calculus applications in signals and systems. Zbl 1172.94301 Ortigueira, Manuel Duarte; Machado, J. A. Tenreiro 29 2006 Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. Zbl 1296.35154 Yang, Xiao-Jun; Baleanu, Dumitru; Machado, José António Tenreiro 28 2013 Systems of Navier-Stokes equations on Cantor sets. Zbl 1299.76047 Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A. 28 2013 Numerical solution of variable-order fractional integro-partial differential equations via sinc collocation method based on single and double exponential transformations. Zbl 1452.65268 Babaei, A.; Moghaddam, B. P.; Banihashemi, S.; Machado, J. A. T. 28 2020 Time domain design of fractional differintegrators using least-squares. Zbl 1172.94364 Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Silva, Manuel F. 27 2006 Local fractional variational iteration and decomposition methods for wave equation on Cantor sets within local fractional operators. Zbl 1468.35226 Baleanu, Dumitru; Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun 26 2014 Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Zbl 1443.93108 Chen, Liping; Huang, Tingwen; Machado, J. A. Tenreiro; Lopes, António M.; Chai, Yi; Wu, Ranchao 25 2019 Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations. Zbl 1443.65257 Zaky, Mahmoud A.; Machado, J. Tenreiro 25 2020 Numerical approach for a class of distributed order time fractional partial differential equations. Zbl 1407.65122 Moghaddam, B. P.; Machado, J. A. Tenreiro; Morgado, M. L. 24 2019 A critical analysis of the Caputo-Fabrizio operator. Zbl 1510.26004 Ortigueira, Manuel D.; Tenreiro Machado, J. 24 2018 Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics. Zbl 1464.65151 Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. 24 2020 Fractional dynamics in DNA. Zbl 1218.92038 Tenreiro Machado, J. A.; Costa, António C.; Quelhas, Maria Dulce 23 2011 Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition. Zbl 1428.34020 Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A. 23 2019 A critical analysis of the conformable derivative. Zbl 1437.26006 Abdelhakim, Ahmed A.; Machado, José A. Tenreiro 23 2019 Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments. Zbl 1481.65196 Nikan, O.; Machado, J. A. Tenreiro; Golbabai, A. 21 2021 Fractional order PD\(^\alpha\) joint control of legged robots. Zbl 1182.70019 Silva, Manuel F.; Machado, J. A. Tenreiro 21 2006 Variable order fractional systems. Zbl 1464.26007 Ortigueira, Manuel D.; Valério, Duarte; Tenreiro Machado, J. 21 2019 A computationally efficient method for tempered fractional differential equations with application. Zbl 1405.65092 Moghaddam, Behrouz Parsa; Tenreiro Machado, J. A.; Babaei, Afshin 20 2018 Numerical evaluation of the fractional Klein-Kramers model arising in molecular dynamics. Zbl 07511421 Nikan, O.; Machado, J. A. Tenreiro; Golbabai, A.; Rashidinia, J. 19 2021 The generalized Kudryashov method for nonlinear space-time fractional partial differential equations of Burgers type. Zbl 1439.35529 Gaber, A. A.; Aljohani, A. F.; Ebaid, A.; Machado, J. Tenreiro 19 2019 Generalized shifted Chebyshev polynomials for fractional optimal control problems. Zbl 1462.49014 Hassani, Hossein; Tenreiro Machado, J. A.; Naraghirad, E. 19 2019 Computational scheme for solving nonlinear fractional stochastic differential equations with delay. Zbl 07123588 Moghaddam, B. P.; Mendes Lopes, A.; Tenreiro Machado, J. A.; Mostaghim, Z. S. 18 2019 Particle swarm optimization with fractional-order velocity. Zbl 1204.90119 Solteiro Pires, E. J.; Tenreiro Machado, J. A.; De Moura Oliveira, P. B.; Boaventura Cunha, J.; Mendes, Luís 18 2010 Application of fractional calculus in the dynamical analysis and control of mechanical manipulators. Zbl 1159.26303 Fonseca Ferreira, N. M.; Duarte, Fernando B.; Lima, Miguel F. M.; Marcos, Maria G.; Machado, J. A. Tenreiro 18 2008 Fractional order dynamics in a GA planner. Zbl 1145.94371 Pires, E. J. Solteiro; Machado, J. A. Tenreiro; De Moura Oliveira, P. B. 18 2003 An extension of estimation of domain of attraction for fractional order linear system subject to saturation control. Zbl 1319.93059 Alaviyan Shahri, Esmat Sadat; Alfi, Alireza; Tenreiro Machado, J. A. 17 2015 Numerical solution of mixed-type fractional functional differential equations using modified Lucas polynomials. Zbl 1449.65143 Moghaddam, B. P.; Dabiri, A.; Lopes, António M.; Machado, J. A. Tenreiro 17 2019 Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model. Zbl 1481.65150 Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. 17 2021 New nonautonomous combined multi-wave solutions for \((2+1)\)-dimensional variable coefficients KdV equation. Zbl 1398.35102 Osman, M. S.; Machado, J. A. T. 16 2018 Optimal tuning of fractional controllers using genetic algorithms. Zbl 1211.93070 Tenreiro Machado, J. A. 16 2010 Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks. Zbl 1443.93101 Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro 16 2019 The \(\psi\)-Hilfer fractional calculus of variable order and its applications. Zbl 1476.26004 Vanterler da C. Sousa, J.; Machado, J. A. Tenreiro; de Oliveira, E. Capelas 16 2020 Sufficient conditions for existence and uniqueness of fractional stochastic delay differential equations. Zbl 1490.60172 Moghaddam, B. P.; Zhang, Lei; Lopes, A. M.; Tenreiro Machado, J. A.; Mostaghim, Z. S. 16 2020 Fractional order electromagnetics. Zbl 1172.94454 Machado, J. A. Tenreiro; Jesus, Isabel S.; Galhano, Alexandra; Boaventura Cunha, J. 15 2006 Numerical investigation of the nonlinear modified anomalous diffusion process. Zbl 1430.60091 Nikan, O.; Tenreiro Machado, J. A.; Golbabai, A.; Nikazad, T. 15 2019 Stability analysis of a class of nonlinear fractional-order systems under control input saturation. Zbl 1391.93177 Shahri, Esmat Sadat Alaviyan; Alfi, Alireza; Machado, J. A. Tenreiro 14 2018 Rhapsody in fractional. Zbl 1314.39007 Tenreiro Machado, J.; Lopes, António M.; Duarte, Fernando B.; Ortigueira, Manuel D.; Rato, Raul T. 14 2014 An innovative fractional order LMS algorithm for power signal parameter estimation. Zbl 1481.94050 Chaudhary, Naveed Ishtiaq; Latif, Rizwan; Zahoor Raja, Muhammad Asif; Machado, J. A. Tenreiro 14 2020 Optimal control of variable-order fractional model for delay cancer treatments. Zbl 1481.92071 Sweilam, N. H.; AL-Mekhlafi, S. M.; Albalawi, A. O.; Tenreiro Machado, J. A. 14 2021 Chebyshev spectral methods for multi-order fractional neutral pantograph equations. Zbl 1516.34016 Ezz-Eldien, S. S.; Wang, Y.; Abdelkawy, M. A.; Zaky, M. A.; Aldraiweesh, A. A.; Machado, J. Tenreiro 14 2020 A new insight into complexity from the local fractional calculus view point: modelling growths of populations. Zbl 1381.92088 Yang, Xiao-Jun; Machado, J. A. Tenreiro 13 2017 Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016). Zbl 1351.26017 Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor 13 2016 A review of power laws in real life phenomena. Zbl 1248.60020 Pinto, Carla M. A.; Mendes Lopes, A.; Tenreiro Machado, J. A. 13 2012 The failure of certain fractional calculus operators in two physical models. Zbl 1427.93054 Ortigueira, Manuel D.; Martynyuk, Valeriy; Fedula, Mykola; Machado, J. Tenreiro 13 2019 Analysis of natural and artificial phenomena using signal processing and fractional calculus. Zbl 1323.92092 Machado, J. A. Tenreiro; Lopes, António M. 13 2015 Fractional generalization of memristor and higher order elements. Zbl 1259.35219 Tenreiro Machado, J. 13 2013 Dynamic stability analysis of fractional order leaky integrator echo state neural networks. Zbl 1510.68097 Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A. 13 2017 Partial chaos suppression in a fractional order macroeconomic model. Zbl 07313625 David, S. A.; Machado, J. A. T.; Quintino, D. D.; Balthazar, J. M. 13 2016 Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay. Zbl 1398.93281 Li, Penghua; Chen, Liping; Wu, Ranchao; Tenreiro Machado, J. A.; Lopes, António M.; Yuan, Liguo 12 2018 Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation. Zbl 07677986 Aghayan, Zahra Sadat; Alfi, Alireza; Machado, J. A. Tenreiro 1 2023 Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations. Zbl 07678011 Abd-Elhameed, Waleed M.; Machado, José A. Tenreiro; Youssri, Youssri H. 7 2022 Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks. Zbl 07636094 Avazzadeh, Zakieh; Nikan, Omid; Tenreiro Machado, José; Rasoulizadeh, Mohammad Navaz 2 2022 Fractional generalization of entropy improves the characterization of rotors in simulated atrial fibrillation. Zbl 1510.92066 Ugarte, Juan P.; Tenreiro Machado, J. A.; Tobón, Catalina 1 2022 Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport. Zbl 1471.65162 Nikan, O.; Avazzadeh, Z.; Machado, J. A. Tenreiro 40 2021 Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments. Zbl 1481.65196 Nikan, O.; Machado, J. A. Tenreiro; Golbabai, A. 21 2021 Numerical evaluation of the fractional Klein-Kramers model arising in molecular dynamics. Zbl 07511421 Nikan, O.; Machado, J. A. Tenreiro; Golbabai, A.; Rashidinia, J. 19 2021 Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model. Zbl 1481.65150 Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. 17 2021 Optimal control of variable-order fractional model for delay cancer treatments. Zbl 1481.92071 Sweilam, N. H.; AL-Mekhlafi, S. M.; Albalawi, A. O.; Tenreiro Machado, J. A. 14 2021 An optimization technique for solving a class of nonlinear fractional optimal control problems: application in cancer treatment. Zbl 1481.49037 Hassani, H.; Machado, J. A. Tenreiro; Mehrabi, S. 11 2021 Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems. Zbl 1481.93148 Chaudhary, Naveed Ishtiaq; Raja, Muhammad Asif Zahoor; He, Yigang; Aslam Khan, Zeshan; Machado, J. A. Tenreiro 9 2021 An integro quadratic spline-based scheme for solving nonlinear fractional stochastic differential equations with constant time delay. Zbl 1455.65017 Moghaddam, B. P.; Mostaghim, Z. S.; Pantelous, Athanasios A.; Machado, J. A. Tenreiro 9 2021 Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population. Zbl 1498.92004 Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. 6 2021 LMI-based stability analysis of fractional order systems of neutral type with time varying delays under actuator saturation. Zbl 1476.34110 Aghayan, Zahra Sadat; Alfi, Alireza; Machado, J. A. Tenreiro 5 2021 Complex-order particle swarm optimization. Zbl 1454.90116 Tenreiro Machado, J. A.; Abedi Pahnehkolaei, Seyed Mehdi; Alfi, Alireza 5 2021 Robust stability analysis of uncertain fractional order neutral-type delay nonlinear systems with actuator saturation. Zbl 1481.93105 Aghayan, Zahra Sadat; Alfi, Alireza; Tenreiro Machado, J. A. 4 2021 Substantial, tempered, and shifted fractional derivatives: three faces of a tetrahedron. Zbl 1470.26012 Ortigueira, Manuel D.; Bengochea, Gabriel; Machado, J. Tenreiro 4 2021 The bouncing ball and the Grünwald-Letnikov definition of fractional derivative. Zbl 1498.26014 Machado, J. A. Tenreiro 3 2021 Numerical solution of nonlinear fractional optimal control problems using generalized Bernoulli polynomials. Zbl 1475.49035 Hassani, Hossein; Machado, José António Tenreiro; Asl, Mohammad Kazem Hosseini; Dahaghin, Mohammad Shafi 3 2021 Multidimensional scaling analysis of generalized mean discrete-time fractional order controllers. Zbl 1458.93114 Lopes, António M.; Machado, J. A. Tenreiro 3 2021 Observer-based control approach for fractional-order delay systems of neutral type with saturating actuator. Zbl 1469.93039 Aghayan, Zahra Sadat; Alfi, Alireza; Machado, Jose Antonio Tenreiro 3 2021 Spontaneous activation under atrial fibrosis: a model using complex order derivatives. Zbl 1457.92046 Ugarte, Juan P.; Tobón, Catalina; Saiz, Javier; Mendes Lopes, António; Machado, José A. Tenreiro 2 2021 Cluster analysis of the large natural satellites in the solar system. Zbl 1481.85006 Mehdipour, S. Hamid; Machado, J. A. Tenreiro 1 2021 Multidimensional scaling and visualization of patterns in distribution of nontrivial zeros of the zeta-function. Zbl 1469.11298 Machado, J. Tenreiro; Luchko, Yuri 1 2021 Numerical solution of variable-order fractional integro-partial differential equations via sinc collocation method based on single and double exponential transformations. Zbl 1452.65268 Babaei, A.; Moghaddam, B. P.; Banihashemi, S.; Machado, J. A. T. 28 2020 Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations. Zbl 1443.65257 Zaky, Mahmoud A.; Machado, J. Tenreiro 25 2020 Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics. Zbl 1464.65151 Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. 24 2020 The \(\psi\)-Hilfer fractional calculus of variable order and its applications. Zbl 1476.26004 Vanterler da C. Sousa, J.; Machado, J. A. Tenreiro; de Oliveira, E. Capelas 16 2020 Sufficient conditions for existence and uniqueness of fractional stochastic delay differential equations. Zbl 1490.60172 Moghaddam, B. P.; Zhang, Lei; Lopes, A. M.; Tenreiro Machado, J. A.; Mostaghim, Z. S. 16 2020 An innovative fractional order LMS algorithm for power signal parameter estimation. Zbl 1481.94050 Chaudhary, Naveed Ishtiaq; Latif, Rizwan; Zahoor Raja, Muhammad Asif; Machado, J. A. Tenreiro 14 2020 Chebyshev spectral methods for multi-order fractional neutral pantograph equations. Zbl 1516.34016 Ezz-Eldien, S. S.; Wang, Y.; Abdelkawy, M. A.; Zaky, M. A.; Aldraiweesh, A. A.; Machado, J. Tenreiro 14 2020 Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation. Zbl 1481.93103 Alaviyan Shahri, Esmat Sadat; Alfi, Alireza; Machado, J. A. Tenreiro 12 2020 Comments on: “The failure of certain fractional calculus operators in two physical models”. Zbl 1437.26008 Baleanu, Dumitru 12 2020 A computational approach for the non-smooth solution of non-linear weakly singular Volterra integral equation with proportional delay. Zbl 1436.65215 Mokhtary, P.; Moghaddam, B. P.; Lopes, A. M.; Machado, J. A. Tenreiro 11 2020 Generalized shifted Chebyshev polynomials: solving a general class of nonlinear variable order fractional PDE. Zbl 1450.35267 Hassani, Hossein; Tenreiro Machado, J. A.; Avazzadeh, Zakieh; Naraghirad, E. 11 2020 An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation. Zbl 1446.65127 Hassani, H.; Machado, J. A. Tenreiro; Naraghirad, E. 8 2020 Generalized Bernoulli polynomials: solving nonlinear 2D fractional optimal control problems. Zbl 1443.93061 Hassani, H.; Machado, J. A. Tenreiro; Avazzadeh, Zakieh; Naraghirad, E.; Dahaghin, M. Sh. 7 2020 Output-feedback-guaranteed cost control of fractional-order uncertain linear delayed systems. Zbl 1463.93078 Chen, Liping; Li, Tingting; Wu, Ranchao; Lopes, António M.; Machado, J. A. Tenreiro; Wu, Kehan 7 2020 Stability analysis of fractional order neutral-type systems considering time varying delays, nonlinear perturbations, and input saturation. Zbl 1455.93147 Aghayan, Zahra Sadat; Alfi, Alireza; Machado, J. A. Tenreiro 6 2020 On the properties of some operators under the perspective of fractional system theory. Zbl 1468.34012 Ortigueira, Manuel D.; Tenreiro Machado, J. 5 2020 Time-fractional dependence of the shear force in some beam type problems with negative Young modulus. Zbl 1481.74429 Cao Labora, Daniel; Lopes, António M.; Machado, J. A. Tenreiro 3 2020 A combined measure to differentiate EEG signals using fractal dimension and MFDFA-Hurst. Zbl 1451.92182 David, S. A.; Machado, J. A. T.; Inácio, C. M. C.; Valentim, C. A. 3 2020 A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Zbl 1488.30224 Moghaddam, B. Parsa; Tenreiro Machado, J. A.; Shajari, Parisa Sattari; Salamat Mostaghim, Zeynab 2 2020 On dual Bernstein polynomials and stochastic fractional integro-differential equations. Zbl 1456.60167 Sayevand, Khosro; Machado, J. Tenreiro; Masti, Iman 2 2020 Fuzzy logic embedding of fractional order sliding mode and state feedback controllers for synchronization of uncertain fractional chaotic systems. Zbl 1449.93164 Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro 2 2020 Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials. Zbl 1476.35310 Hassani, H.; Machado, J. A. Tenreiro; Naraghirad, E.; Sadeghi, B. 2 2020 Generalized Newtonian fractional model for the vertical motion of a particle. Zbl 1481.70002 Elzahar, E. R.; Gaber, A. A.; Aljohani, A. F.; Machado, J. Tenreiro; Ebaid, A. 1 2020 Fractional fractals. Zbl 1488.28018 Tenreiro Machado, J. A.; Cao Labora, Daniel 1 2020 Fractional-order modelling of epoxy resin. Zbl 1462.82087 Machado, J. A. Tenreiro; Lopes, António M.; De Camposinhos, Rui 1 2020 Application of the Euler and Runge-Kutta generalized methods for FDE and symbolic packages in the analysis of some fractional attractors. Zbl 07201330 Milici, Constantin; Machado, José Tenreiro; Drăgănescu, Gheorghe 1 2020 Nonlinear dynamics and control. Proceedings of the first international nonlinear dynamics conference, NODYCON 2019, Rome, Italy, February 17–20, 2019. Volume II. Zbl 1454.93003 1 2020 Nonlinear dynamics of structures, systems and devices. Proceedings of the first international nonlinear dynamics conference, NODYCON 2019, Rome, Italy, February 17–20, 2019. Volume I. Zbl 1464.70003 1 2020 Multidimensional scaling and visualization of patterns in prime numbers. Zbl 1476.11123 Machado, J. Tenreiro; Lopes, António M. 1 2020 Numerical solutions of realistic nonlinear phenomena. Selected papers of the international conference on applied mathematics in engineering (ICAME’18), Burhaniye, Turkey, June 27–29, 2018. Zbl 1448.65009 1 2020 A review of definitions of fractional derivatives and other operators. Zbl 1452.26008 Sales Teodoro, G.; Tenreiro Machado, J. A.; de Oliveira, E. Capelas 86 2019 A new fractal nonlinear Burgers’ equation arising in the acoustic signals propagation. Zbl 1435.35412 Yang, Xiao-Jun; Machado, J. A. Tenreiro 47 2019 Introduction to fractional differential equations. Zbl 1417.34004 Milici, Constantin; Drăgănescu, Gheorghe; Machado, José António Tenreiro 29 2019 Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Zbl 1443.93108 Chen, Liping; Huang, Tingwen; Machado, J. A. Tenreiro; Lopes, António M.; Chai, Yi; Wu, Ranchao 25 2019 Numerical approach for a class of distributed order time fractional partial differential equations. Zbl 1407.65122 Moghaddam, B. P.; Machado, J. A. Tenreiro; Morgado, M. L. 24 2019 Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition. Zbl 1428.34020 Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A. 23 2019 A critical analysis of the conformable derivative. Zbl 1437.26006 Abdelhakim, Ahmed A.; Machado, José A. Tenreiro 23 2019 Variable order fractional systems. Zbl 1464.26007 Ortigueira, Manuel D.; Valério, Duarte; Tenreiro Machado, J. 21 2019 The generalized Kudryashov method for nonlinear space-time fractional partial differential equations of Burgers type. Zbl 1439.35529 Gaber, A. A.; Aljohani, A. F.; Ebaid, A.; Machado, J. Tenreiro 19 2019 Generalized shifted Chebyshev polynomials for fractional optimal control problems. Zbl 1462.49014 Hassani, Hossein; Tenreiro Machado, J. A.; Naraghirad, E. 19 2019 Computational scheme for solving nonlinear fractional stochastic differential equations with delay. Zbl 07123588 Moghaddam, B. P.; Mendes Lopes, A.; Tenreiro Machado, J. A.; Mostaghim, Z. S. 18 2019 Numerical solution of mixed-type fractional functional differential equations using modified Lucas polynomials. Zbl 1449.65143 Moghaddam, B. P.; Dabiri, A.; Lopes, António M.; Machado, J. A. Tenreiro 17 2019 Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks. Zbl 1443.93101 Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro 16 2019 Numerical investigation of the nonlinear modified anomalous diffusion process. Zbl 1430.60091 Nikan, O.; Tenreiro Machado, J. A.; Golbabai, A.; Nikazad, T. 15 2019 The failure of certain fractional calculus operators in two physical models. Zbl 1427.93054 Ortigueira, Manuel D.; Martynyuk, Valeriy; Fedula, Mykola; Machado, J. Tenreiro 13 2019 A new non-standard finite difference method for analyzing the fractional Navier-Stokes equations. Zbl 1442.65177 Sayevand, K.; Machado, J. Tenreiro; Moradi, V. 11 2019 An effective numerical method for solving nonlinear variable-order fractional functional boundary value problems through optimization technique. Zbl 1430.34005 Hassani, H.; Machado, J. A. Tenreiro; Avazzadeh, Z. 10 2019 A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains. Zbl 1449.65164 Azin, H.; Mohammadi, F.; Machado, J. A. Tenreiro 9 2019 Fractional calculus. Selected papers from the international conference on fractional differentiation and its applications (ICFDA 2018), Amman, Jordan, July 16–18, 2018. Zbl 1444.26001 8 2019 Fractional derivatives and negative probabilities. Zbl 1522.26007 Tenreiro Machado, J. 6 2019 On the numerical computation of the Mittag-Leffler function. Zbl 07168325 Ortigueira, Manuel D.; Lopes, António M.; Tenreiro Machado, José 5 2019 Ranking the scientific output of researchers in fractional calculus. Zbl 1426.26016 Machado, J. A. Tenreiro; Lopes, António M. 2 2019 Information analysis of the human DNA. Zbl 1430.92062 Machado, J. Tenreiro 2 2019 Fractional-order modeling of a diode. Zbl 1464.82023 Tenreiro Machado, J. A.; Lopes, António M. 2 2019 A survey on fractional asymptotic expansion method: a forgotten theory. Zbl 1437.34014 Sayevand, Khosro; Machado, José A. Tenreiro 1 2019 An algorithm for the approximate solution of the fractional Riccati differential equation. Zbl 07168320 Ezz-Eldien, S. S.; Machado, J. A. T.; Wang, Y.; Aldraiweesh, A. A. 1 2019 Analysis of the two-dimensional fractional projectile motion in view of the experimental data. Zbl 1430.70003 Ebaid, A.; El-Zahar, E. R.; Aljohani, A. F.; Salah, Bashir; Krid, Mohammed; Machado, J. Tenreiro 1 2019 Mathematical and computational modeling of political systems. Zbl 1437.91383 Machado, J. Tenreiro 1 2019 On the fractional Cornu spirals. Zbl 1508.68418 Milici, Constantin; Tenreiro Machado, J.; Drăgănescu, Gheorghe 1 2019 The Lorentz transformations and one observation in the perspective of fractional calculus. Zbl 1476.83002 Cao Labora, Daniel; Lopes, António M.; Tenreiro Machado, J. A. 1 2019 A computational perspective of the periodic table of elements. Zbl 1476.62022 Tenreiro Machado, J.; Lopes, António M. 1 2019 Multidimensional scaling analysis of the solar system objects. Zbl 1522.85006 Tenreiro Machado, J.; Mehdipour, S. Hamid 1 2019 Optimal variable-order fractional PID controllers for dynamical systems. Zbl 1392.49033 Dabiri, A.; Moghaddam, B. P.; Machado, J. A. Tenreiro 52 2018 A spectral framework for fractional variational problems based on fractional Jacobi functions. Zbl 06902342 Zaky, M. A.; Doha, E. H.; Tenreiro Machado, J. A. 35 2018 A critical analysis of the Caputo-Fabrizio operator. Zbl 1510.26004 Ortigueira, Manuel D.; Tenreiro Machado, J. 24 2018 A computationally efficient method for tempered fractional differential equations with application. Zbl 1405.65092 Moghaddam, Behrouz Parsa; Tenreiro Machado, J. A.; Babaei, Afshin 20 2018 New nonautonomous combined multi-wave solutions for \((2+1)\)-dimensional variable coefficients KdV equation. Zbl 1398.35102 Osman, M. S.; Machado, J. A. T. 16 2018 Stability analysis of a class of nonlinear fractional-order systems under control input saturation. Zbl 1391.93177 Shahri, Esmat Sadat Alaviyan; Alfi, Alireza; Machado, J. A. Tenreiro 14 2018 Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay. Zbl 1398.93281 Li, Penghua; Chen, Liping; Wu, Ranchao; Tenreiro Machado, J. A.; Lopes, António M.; Yuan, Liguo 12 2018 Stabilization of uncertain multi-order fractional systems based on the extended state observer. Zbl 1398.93306 Chen, Liping; Chen, Gang; Wu, Ranchao; Machado, J. A. Tenreiro; Lopes, António M.; Ge, Suoliang 10 2018 A new operational approach for solving fractional variational problems depending on indefinite integrals. Zbl 07263284 Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T. 10 2018 Robust stability and stabilization of uncertain fractional order systems subject to input saturation. Zbl 1400.93252 Alaviyan Shahri, Esmat Sadat; Alfi, Alireza; Tenreiro Machado, J. A. 8 2018 Fractional dynamic behavior in ethanol prices series. Zbl 1462.62717 David, S. A.; Quintino, D. D.; Inacio, C. M. C. jun.; Machado, J. A. T. 6 2018 Fractional-order model of wine. Zbl 1386.78019 Lopes, António M.; Tenreiro Machado, J. A.; Ramalho, Elisa 3 2018 An accurate and cost-efficient numerical approach to analyze the initial and boundary value problems of fractional multi-order. Zbl 1424.65100 Sayevand, K.; Machado, J. Tenreiro 2 2018 A new glance on the Leibniz rule for fractional derivatives. Zbl 1470.34027 Sayevand, K.; Tenreiro Machado, J.; Baleanu, D. 1 2018 ...and 168 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,392 Authors 180 Machado, José António Tenreiro 178 Băleanu, Dumitru I. 93 Ahmad, Bashir 55 Ntouyas, Sotiris K. 44 Al-saedi, Ahmed Eid Salem 41 Abdeljawad, Thabet 39 Lopes, António M. 39 Tarasov, Vasily E. 38 Yang, Xiao-Jun 35 Nieto Roig, Juan Jose 34 Zaky, Mahmoud A. 33 Wang, Jinrong 32 Agarwal, Ravi P. 32 Benchohra, Mouffak 30 de Oliveira, Edmundo Capelas 29 Avazzadeh, Zakieh 28 Shah, Kamal 28 Wang, Guotao 27 Torres, Delfim Fernando Marado 27 Vanterler da Costa Sousa, José 25 Chen, Yangquan 25 Heydari, Mohammad Hossein 24 Razzaghi, Mohsen 23 Ibrahim, Rabha Waell 22 Abdelkawy, Mohamed A. 22 Luca, Rodica 22 Nikan, Omid 22 Zhang, Lihong 21 Agarwal, Praveen 21 Cao, Jinde 21 Jafari, Hossein 21 Kumar, Devendra 21 Ordokhani, Yadollah 21 Trujillo, Juan J. 19 Doha, Eid H. 19 Sayevand, Khosro 19 Singh, Jagdev 18 Atangana, Abdon 18 Bhrawy, Ali Hassan 18 Moghaddam, Behrouz Parsa 18 Zhou, Yong 16 Cattani, Carlo 16 Salahshour, Soheil 16 Veeresha, Pundikala 15 Alfi, Alireza 15 Baskonus, Haci Mehmet 15 Gómez-Aguilar, José Francisco 15 Henderson, Johnny Lee 15 Rezapour, Shahram 15 Shang, Pengjian 15 Srivastava, Hari Mohan 15 Tavazoei, Mohammad Saleh 14 Ahmadian, Ali 14 Ezz-Eldien, Samer S. 14 Fernandez, Arran 14 Hendy, Ahmed S. 14 Jarad, Fahd 14 Liu, Fawang 14 Momani, Shaher M. 14 Tariboon, Jessada 14 Usman, Muhammad 14 Zada, Akbar 13 Abdo, Mohammed Salem 13 Balachandran, Krishnan 13 Haeri, Mohammad 13 Raja, Muhammad Asif Zahoor 13 Youssri, Youssri H. 13 Zhao, Yang 12 Abbas, Said 12 Akgül, Ali 12 Bettayeb, Maamar 12 Hassani, Hossein 12 Ortigueira, Manuel D. 12 Salim, Abdelkrim 12 Yu, Yongguang 11 Dehghan Takht Fooladi, Mehdi 11 Golmankhaneh, Alireza Khalili 11 Hamid, Muhammad 11 Khan, Rahmat Ali 11 Kumar, Sunil 11 Lazreg, Jamal Eddine 11 Li, Changpin 11 Lu, Junguo 11 Malik, Salman A. 11 Qiu, Wenlin 11 Sabatier, Jocelyn 11 Vijayakumar, Velusamy 11 Wang, Yong 11 Xu, Da 10 Almeida, Ricardo 10 Barbosa, Ramiro S. 10 Fečkan, Michal 10 Inc, Mustafa 10 Malinowska, Agnieszka Barbara 10 O’Regan, Donal 10 Prakasha, Doddabhadrappla Gowda 10 Ravichandran, Chokkalingam 10 Saha Ray, Santanu 10 Xu, Wei 9 Abd-Elhameed, Waleed Mohamed ...and 5,292 more Authors all top 5 Cited in 376 Serials 222 Advances in Difference Equations 170 Nonlinear Dynamics 161 Computational and Applied Mathematics 159 Chaos, Solitons and Fractals 156 Communications in Nonlinear Science and Numerical Simulation 149 Fractional Calculus & Applied Analysis 132 Applied Mathematics and Computation 106 Computers & Mathematics with Applications 99 Fractals 98 Abstract and Applied Analysis 88 Mathematical Methods in the Applied Sciences 81 Journal of Computational and Applied Mathematics 70 Mathematical Problems in Engineering 59 Applied Mathematical Modelling 52 Physica A 52 International Journal of Applied and Computational Mathematics 49 Applied Numerical Mathematics 49 Journal of Function Spaces 44 International Journal of Nonlinear Sciences and Numerical Simulation 42 Mathematics and Computers in Simulation 39 Journal of the Franklin Institute 39 Journal of Applied Mathematics and Computing 38 Numerical Methods for Partial Differential Equations 36 Advances in Mathematical Physics 34 Boundary Value Problems 31 AIMS Mathematics 30 Discrete Dynamics in Nature and Society 29 Journal of Nonlinear Science and Applications 29 International Journal of Systems Science. 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Serie II 8 Optimal Control Applications & Methods 8 Lobachevskii Journal of Mathematics 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 8 Mathematical Modelling of Natural Phenomena 8 Tbilisi Mathematical Journal 8 Journal of Applied Analysis and Computation 8 Evolution Equations and Control Theory 8 Communications on Applied Mathematics and Computation 7 International Journal of Control 7 Physics Letters. 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