Compute Distance To:
 Documents Indexed: 287 Publications since 1978, including 3 Books 27 Contributions as Editor · 2 Further Contributions Biographic References: 1 Publication Co-Authors: 195 Co-Authors with 272 Joint Publications 5,904 Co-Co-Authors
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### Co-Authors

 36 single-authored 37 Lopes, António M. 26 Băleanu, Dumitru I. 17 Barbosa, Ramiro S. 14 Alfi, Alireza 14 Yang, Xiao-Jun 13 Jesus, Isabel S. 13 Moghaddam, Behrouz Parsa 12 Ortigueira, Manuel D. 11 Galhano, Alexandra M. S. F. 10 Silva, Manuel F. 9 Duarte, Fernando B. M. 9 Hassani, Hossein 9 Kiryakova, Virginia S. 7 Bhrawy, Ali Hassan 7 Chen, Liping 7 de Moura Oliveira, Paulo B. 7 Sayevand, Khosro 7 Wu, Ranchao 6 Avazzadeh, Zakieh 6 Nikan, Omid 6 Pahnehkolaei, Seyed Mehdi Abedi 5 Costa, António C. 5 Figueiredo, Lino B. 5 Luo, Albert C. J. 5 Mainardi, Francesco 5 Naraghirad, Eskandar 5 Valério, Duarte 5 Zaky, Mahmoud A. 4 Aghayan, Zahra Sadat 4 Alaviyan Shahri, Esmat Sadat 4 Boaventura-Cunha, José 4 da Graça Marcos, Maria 4 Ebaid, Abdelhalim 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 Balachandran, Balakumar 3 Behl, Ramandeep 3 Cao Labora, Daniel 3 Cattani, Carlo 3 David, Sergio Adriani 3 de Oliveira, Edmundo Capelas 3 Doha, Eid H. 3 Drăgănescu, Gheorghe 3 Ezz-Eldien, Samer S. 3 Fonseca Ferreira, Nuno Miguel 3 Golbabai, Ahmad 3 Ionescu, Clara Mihaela 3 Lacarbonara, Walter 3 Milici, Constantin 3 Monteiro Duarte, Gonçalo 3 Pires, E. J. Solteiro 3 Reis, Cecília M. 3 Rivero, Margarita 3 Rosário, João Maurıcio 3 Srivastava, Hari Mohan 3 Stépán, Gábor 3 Tar, József K. 2 Abelha, António 2 Alshomrani, Ali Saleh 2 Babaei, Afshin 2 Chaudhary, Naveed Ishtiaq 2 Chen, Wen 2 Copot, Dana 2 De Keyser, Robin 2 Faustino, Ana M. 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 Júdice, Joaquim João 2 Liu, Fawang 2 Luchko, Yuri 2 Marcos, Maria G. 2 Martynyuk, Valeriy 2 Masti, Iman 2 Mehdipour, S. Hamid 2 Mostaghim, Zeinab Salamat 2 Neves, José 2 Nigmatullin, Raoul R. 2 Özdemir, Necati 2 Pan, Wei 2 Quintino, D. D. 2 Raja, Muhammad Asif Zahoor 2 Tobón, Catalina 2 Ugarte, Juan P. 2 Volchenkov, Dimitri Yu. 2 Zhou, Yong 1 Abdelhakim, Ahmed A. 1 Abdelkawy, Mohamed A. 1 Afraimovich, Valentin S. 1 Agarwal, Praveen 1 Agrawal, Om Prakash ...and 105 more Co-Authors
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### Serials

 46 Communications in Nonlinear Science and Numerical Simulation 28 Nonlinear Dynamics 27 Fractional Calculus & Applied Analysis 16 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 7 Signal Processing 7 Nonlinear Systems and Complexity 6 Mathematical Methods in the Applied Sciences 5 Applied Mathematics and Computation 5 International Journal of Nonlinear Sciences and Numerical Simulation 4 Journal of Computational Physics 4 Chaos, Solitons and Fractals 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 3 Neural Networks 3 Asian Journal of Control 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 Mathematics and Computers in Simulation 1 Portugaliae Mathematica 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 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
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### Fields

 118 Real functions (26-XX) 72 Ordinary differential equations (34-XX) 71 Systems theory; control (93-XX) 57 Numerical analysis (65-XX) 46 Partial differential equations (35-XX) 33 Mechanics of particles and systems (70-XX) 33 Biology and other natural sciences (92-XX) 29 General and overarching topics; collections (00-XX) 27 Information and communication theory, circuits (94-XX) 23 Dynamical systems and ergodic theory (37-XX) 20 Operations research, mathematical programming (90-XX) 17 Statistics (62-XX) 16 Computer science (68-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Probability theory and stochastic processes (60-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 11 Mechanics of deformable solids (74-XX) 11 Optics, electromagnetic theory (78-XX) 10 History and biography (01-XX) 8 Measure and integration (28-XX) 8 Special functions (33-XX) 7 Operator theory (47-XX) 7 Fluid mechanics (76-XX) 7 Geophysics (86-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Approximations and expansions (41-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral equations (45-XX) 4 Mathematics education (97-XX) 3 Combinatorics (05-XX) 3 Number theory (11-XX) 3 Integral transforms, operational calculus (44-XX) 3 Classical thermodynamics, heat transfer (80-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) 2 Astronomy and astrophysics (85-XX) 1 Topological groups, Lie groups (22-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

226 Publications have been cited 3,842 times in 2,631 Documents Cited by Year
Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Zbl 1116.00014
2007
Recent history of fractional calculus. Zbl 1221.26002
Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco
2011
Analysis and design of fractional-order digital control systems. Zbl 0875.93154
1997
What is a fractional derivative? Zbl 1349.26016
Ortigueira, Manuel D.; Tenreiro Machado, J. A.
2015
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
2010
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
2012
Discrete-time fractional-order controllers. Zbl 1111.93307
2001
A review of operational matrices and spectral techniques for fractional calculus. Zbl 1348.65106
Bhrawy, Ali H.; Taha, Taha M.; Tenreiro Machado, José A.
2015
Fractional control of heat diffusion systems. Zbl 1210.80008
Jesus, Isabel S.; Tenreiro Machado, J. A.
2008
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.
2010
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
2016
A review of definitions for fractional derivatives and integral. Zbl 1407.26013
de Oliveira, Edmundo Capelas; Tenreiro Machado, José António
2014
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.
2007
Optimal variable-order fractional PID controllers for dynamical systems. Zbl 1392.49033
2018
Tuning of PID controllers based on Bode’s ideal transfer function. Zbl 1134.93334
Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Ferreira, Isabel M.
2004
A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010
2003
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.
2017
Some pioneers of the applications of fractional calculus. Zbl 1305.26008
Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia
2014
A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels. Zbl 1376.65159
2017
Historical survey: the chronicles of fractional calculus. Zbl 1364.26002
Machado, J. A. Tenreiro; Kiryakova, Virginia
2017
Extended algorithms for approximating variable order fractional derivatives with applications. Zbl 1370.26017
2017
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
2010
And I say to myself: “What a fractional world!”. Zbl 1273.37002
2011
Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators. Zbl 1027.70011
Duarte, Fernando B. M.; Machado, J. A. Tenreiro
2002
A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations. Zbl 1412.65084
2017
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.
2015
Stability of fractional order systems. Zbl 1296.93172
Rivero, Margarita; Rogosin, Sergei V.; Machado, José A. Tenreiro; Trujillo, Juan J.
2013
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.
2013
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
2010
An integro quadratic spline approach for a class of variable-order fractional initial value problems. Zbl 1422.65131
2017
A new family of the local fractional PDEs. Zbl 1386.35461
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Nieto, Juan J.
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.
2016
Fractional order calculus: basic concepts and engineering applications. Zbl 1190.26002
Gutiérrez, Ricardo Enrique; Rosário, João Maurício; Tenreiro Machado, José
2010
A new fractal nonlinear Burgers’ equation arising in the acoustic signals propagation. Zbl 1435.35412
Yang, Xiao-Jun; Machado, J. A. Tenreiro
2019
Fractional electrical impedances in botanical elements. Zbl 1229.78023
Jesus, Isabel S.; Tenreiro Machado, J. A.; Cunha, J. Boaventure
2008
Fractional-order control of a hexapod robot. Zbl 1096.70004
Silva, Manuel F.; Machado, J. A. T.; Lopes, A. M.
2004
Development of fractional order capacitors based on electrolyte processes. Zbl 1173.78313
Jesus, Isabel S.; Tenreiro Machado, J. A.
2009
A spectral framework for fractional variational problems based on fractional Jacobi functions. Zbl 06902342
Zaky, M. A.; Doha, E. H.; Tenreiro Machado, J. A.
2018
Entropy analysis of integer and fractional dynamical systems. Zbl 1211.37057
2010
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.
2016
Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. Zbl 1354.35180
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Hristov, Jordan
2016
A review of definitions of fractional derivatives and other operators. Zbl 1452.26008
Sales Teodoro, G.; Tenreiro Machado, J. A.; de Oliveira, E. Capelas
2019
Time domain design of fractional differintegrators using least-squares. Zbl 1172.94364
Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Silva, Manuel F.
2006
Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011
Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia
2015
Systems of Navier-Stokes equations on Cantor sets. Zbl 1299.76047
Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.
2013
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
2017
Science metrics on fractional calculus development since 1966. Zbl 1312.26004
Machado, J. Tenreiro; Galhano, Alexandra M.; Trujillo, Juan J.
2013
Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. Zbl 1296.35154
Yang, Xiao-Jun; Baleanu, Dumitru; Machado, José António Tenreiro
2013
SM-algorithms for approximating the variable-order fractional derivative of high order. Zbl 1377.65031
2017
Editorial: Fractional calculus applications in signals and systems. Zbl 1172.94301
Ortigueira, Manuel Duarte; Machado, J. A. Tenreiro
2006
Fractional dynamics in DNA. Zbl 1218.92038
Tenreiro Machado, J. A.; Costa, António C.; Quelhas, Maria Dulce
2011
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
2014
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
2008
Numerical approach for a class of distributed order time fractional partial differential equations. Zbl 1407.65122
2019
Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport. Zbl 1471.65162
2021
Optimal tuning of fractional controllers using genetic algorithms. Zbl 1211.93070
2010
Fractional order PD$$^\alpha$$ joint control of legged robots. Zbl 1182.70019
Silva, Manuel F.; Machado, J. A. Tenreiro
2006
Fractional order dynamics in a GA planner. Zbl 1145.94371
Pires, E. J. Solteiro; Machado, J. A. Tenreiro; De Moura Oliveira, P. B.
2003
Rhapsody in fractional. Zbl 1314.39007
Tenreiro Machado, J.; Lopes, António M.; Duarte, Fernando B.; Ortigueira, Manuel D.; Rato, Raul T.
2014
Numerical solution of variable-order fractional integro-partial differential equations via sinc collocation method based on single and double exponential transformations. Zbl 1452.65268
2020
Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics. Zbl 1464.65151
2020
An extension of estimation of domain of attraction for fractional order linear system subject to saturation control. Zbl 1319.93059
2015
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.
2019
New nonautonomous combined multi-wave solutions for $$(2+1)$$-dimensional variable coefficients KdV equation. Zbl 1398.35102
Osman, M. S.; Machado, J. A. T.
2018
A computationally efficient method for tempered fractional differential equations with application. Zbl 1405.65092
2018
Fractional generalization of memristor and higher order elements. Zbl 1259.35219
2013
On the formulation and numerical simulation of distributed-order fractional optimal control problems. Zbl 07261224
Zaky, M. A.; Tenreiro Machado, J. A.
2017
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
2019
Describing function of two masses with backlash. Zbl 1204.70022
Duarte, Fernando B.; Tenreiro Machado, J.
2009
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
2010
A review of power laws in real life phenomena. Zbl 1248.60020
Pinto, Carla M. A.; Mendes Lopes, A.; Tenreiro Machado, J. A.
2012
Fractional order electromagnetics. Zbl 1172.94454
Machado, J. A. Tenreiro; Jesus, Isabel S.; Galhano, Alexandra; Boaventura Cunha, J.
2006
Analysis of natural and artificial phenomena using signal processing and fractional calculus. Zbl 1323.92092
Machado, J. A. Tenreiro; Lopes, António M.
2015
Introduction to fractional differential equations. Zbl 1417.34004
Milici, Constantin; Drăgănescu, Gheorghe; Machado, José António Tenreiro
2019
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
2016
Dynamics of the dow Jones and the NASDAQ stock indexes. Zbl 1204.91110
Duarte, Fernando B.; Tenreiro Machado, J. A.; Monteiro Duarte, Gonçalo
2010
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.
2019
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
2017
Variable order fractional systems. Zbl 1464.26007
Ortigueira, Manuel D.; Valério, Duarte; Tenreiro Machado, J.
2019
A critical analysis of the conformable derivative. Zbl 1437.26006
Abdelhakim, Ahmed A.; Machado, José A. Tenreiro
2019
Approximating fractional derivatives in the perspective of system control. Zbl 1204.93060
Tenreiro Machado, J. A.; Galhano, Alexandra
2009
Describing function analysis of systems with impacts and blacklash. Zbl 1030.70012
Barbosa, R. S.; Machado, J. A. Tenreiro
2002
Fractional-order derivative approximations in discrete-time control systems. Zbl 0979.93519
1999
Chaos suppression in fractional systems using adaptive fractional state feedback control. Zbl 1375.93061
Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro
2017
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
2019
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
2018
Approximating fractional derivatives through the generalized mean. Zbl 1221.26012
Tenreiro Machado, J. A.; Galhano, Alexandra M.; Oliveira, Anabela M.; Tar, József K.
2009
Calculation of fractional derivatives of noisy data with genetic algorithms. Zbl 1176.94016
2009
Control of a heat diffusion system through a fractional order nonlinear algorithm. Zbl 1189.93047
Jesus, Isabel S.; Tenreiro Machado, J. A.; Barbosa, Ramiro S.
2010
A critical analysis of the Caputo-Fabrizio operator. Zbl 07263368
Ortigueira, Manuel D.; Tenreiro Machado, J.
2018
A new numerical technique for local fractional diffusion equation in fractal heat transfer. Zbl 1374.76210
Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Gao, Feng
2016
Jacobi collocation approximation for solving multi-dimensional Volterra integral equations. Zbl 1401.65148
Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; Bhrawy, Ali H.; Tenreiro Machado, José A.; Lopes, António M.
2017
Fractional-order impulse response of the respiratory system. Zbl 1228.65251
Ionescu, Clara; Tenreiro Machado, José; De Keyser, Robin
2011
Entropy analysis of the DNA code dynamics in human chromosomes. Zbl 1228.94032
Tenreiro Machado, J. A.; Costa, António C.; Quelhas, Maria Dulce
2011
Fractional dynamics of a system with particles subjected to impacts. Zbl 1231.82044
2011
Time-delay and fractional derivatives. Zbl 1213.26009
2011
Numerical investigation of the nonlinear modified anomalous diffusion process. Zbl 1430.60091
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
2019
Generalized shifted Chebyshev polynomials: solving a general class of nonlinear variable order fractional PDE. Zbl 1450.35267
2020
Stability analysis of a class of nonlinear fractional-order systems under control input saturation. Zbl 1391.93177
2018
Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport. Zbl 1471.65162
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
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.
2021
Complex-order particle swarm optimization. Zbl 1454.90116
Tenreiro Machado, J. A.; Abedi Pahnehkolaei, Seyed Mehdi; Alfi, Alireza
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.
2021
Multidimensional scaling analysis of generalized mean discrete-time fractional order controllers. Zbl 1458.93114
Lopes, António M.; Machado, J. A. Tenreiro
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.
2021
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model. Zbl 1481.65150
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
2020
Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics. Zbl 1464.65151
2020
Generalized shifted Chebyshev polynomials: solving a general class of nonlinear variable order fractional PDE. Zbl 1450.35267
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
2020
Comments on: “The failure of certain fractional calculus operators in two physical models”. Zbl 1437.26008
Baleanu, Dumitru
2020
An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation. Zbl 1446.65127
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
2020
Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations. Zbl 1443.65257
Zaky, Mahmoud A.; Machado, J. Tenreiro
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
2020
On the properties of some operators under the perspective of fractional system theory. Zbl 1468.34012
Ortigueira, Manuel D.; Tenreiro Machado, J.
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
2020
Stability analysis of fractional order neutral-type systems considering time varying delays, nonlinear perturbations, and input saturation. Zbl 1455.93147
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
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
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.
2020
Multidimensional scaling and visualization of patterns in prime numbers. Zbl 1476.11123
Machado, J. Tenreiro; Lopes, António M.
2020
Generalized Bernoulli polynomials: solving nonlinear 2D fractional optimal control problems. Zbl 1443.93061
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
2020
On dual Bernstein polynomials and stochastic fractional integro-differential equations. Zbl 1456.60167
Sayevand, Khosro; Machado, J. Tenreiro; Masti, Iman
2020
Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials. Zbl 1476.35310
2020
Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation. Zbl 1481.93103
2020
A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Zbl 07419734
Moghaddam, B. Parsa; Tenreiro Machado, J. A.; Shajari, Parisa Sattari; Salamat Mostaghim, Zeynab
2020
A new fractal nonlinear Burgers’ equation arising in the acoustic signals propagation. Zbl 1435.35412
Yang, Xiao-Jun; Machado, J. A. Tenreiro
2019
A review of definitions of fractional derivatives and other operators. Zbl 1452.26008
Sales Teodoro, G.; Tenreiro Machado, J. A.; de Oliveira, E. Capelas
2019
Numerical approach for a class of distributed order time fractional partial differential equations. Zbl 1407.65122
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.
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
2019
Introduction to fractional differential equations. Zbl 1417.34004
Milici, Constantin; Drăgănescu, Gheorghe; Machado, José António Tenreiro
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.
2019
Variable order fractional systems. Zbl 1464.26007
Ortigueira, Manuel D.; Valério, Duarte; Tenreiro Machado, J.
2019
A critical analysis of the conformable derivative. Zbl 1437.26006
Abdelhakim, Ahmed A.; Machado, José A. Tenreiro
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
2019
Numerical investigation of the nonlinear modified anomalous diffusion process. Zbl 1430.60091
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
2019
A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains. Zbl 1449.65164
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
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
2019
An effective numerical method for solving nonlinear variable-order fractional functional boundary value problems through optimization technique. Zbl 1430.34005
2019
Generalized shifted Chebyshev polynomials for fractional optimal control problems. Zbl 1462.49014
2019
Fractional derivatives and negative probabilities. Zbl 07264540
2019
A new non-standard finite difference method for analyzing the fractional Navier-Stokes equations. Zbl 1442.65177
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
2019
On the numerical computation of the Mittag-Leffler function. Zbl 07168325
Ortigueira, Manuel D.; Lopes, António M.; Tenreiro Machado, José
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
2019
Information analysis of the human DNA. Zbl 1430.92062
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.
2019
A computational perspective of the periodic table of elements. Zbl 1476.62022
Tenreiro Machado, J.; Lopes, António M.
2019
Multidimensional scaling analysis of the solar system objects. Zbl 07264550
Tenreiro Machado, J.; Mehdipour, S. Hamid
2019
Fractional-order modeling of a diode. Zbl 1464.82023
Tenreiro Machado, J. A.; Lopes, António M.
2019
Ranking the scientific output of researchers in fractional calculus. Zbl 1426.26016
Machado, J. A. Tenreiro; Lopes, António M.
2019
A survey on fractional asymptotic expansion method: a forgotten theory. Zbl 1437.34014
Sayevand, Khosro; Machado, José A. Tenreiro
2019
Optimal variable-order fractional PID controllers for dynamical systems. Zbl 1392.49033
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.
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.
2018
A computationally efficient method for tempered fractional differential equations with application. Zbl 1405.65092
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
2018
A critical analysis of the Caputo-Fabrizio operator. Zbl 07263368
Ortigueira, Manuel D.; Tenreiro Machado, J.
2018
Stability analysis of a class of nonlinear fractional-order systems under control input saturation. Zbl 1391.93177
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
2018
Robust stability and stabilization of uncertain fractional order systems subject to input saturation. Zbl 1400.93252
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.
2018
Fractional-order model of wine. Zbl 1386.78019
Lopes, António M.; Tenreiro Machado, J. A.; Ramalho, Elisa
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.
2018
An accurate and cost-efficient numerical approach to analyze the initial and boundary value problems of fractional multi-order. Zbl 1424.65100
2018
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.
2017
A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels. Zbl 1376.65159
2017
Historical survey: the chronicles of fractional calculus. Zbl 1364.26002
Machado, J. A. Tenreiro; Kiryakova, Virginia
2017
Extended algorithms for approximating variable order fractional derivatives with applications. Zbl 1370.26017
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
2017
An integro quadratic spline approach for a class of variable-order fractional initial value problems. Zbl 1422.65131
2017
A new family of the local fractional PDEs. Zbl 1386.35461
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Nieto, Juan J.
2017
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
2017
SM-algorithms for approximating the variable-order fractional derivative of high order. Zbl 1377.65031
2017
On the formulation and numerical simulation of distributed-order fractional optimal control problems. Zbl 07261224
Zaky, M. A.; Tenreiro Machado, J. A.
2017
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
2017
Chaos suppression in fractional systems using adaptive fractional state feedback control. Zbl 1375.93061
Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. Tenreiro
2017
Jacobi collocation approximation for solving multi-dimensional Volterra integral equations. Zbl 1401.65148
Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; Bhrawy, Ali H.; Tenreiro Machado, José A.; Lopes, António M.
2017
On a fractal LC-electric circuit modeled by local fractional calculus. Zbl 07257489
Yang, Xiao-Jun; Tenreiro Machado, J. A.; Cattani, Carlo; Gao, Feng
2017
Generation of a family of fractional order hyper-chaotic multi-scroll attractors. Zbl 1380.34119
Chen, Liping; Pan, Wei; Wang, Kunpeng; Wu, Ranchao; Machado, J. A. Tenreiro; Lopes, António M.
2017
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
2017
A fractional perspective on the trajectory control of redundant and hyper-redundant robot manipulators. Zbl 1443.70014
Tenreiro Machado, J. A.; Lopes, António M.
2017
Multidimensional scaling analysis of soccer dynamics. Zbl 1446.62338
Tenreiro Machado, J. A.; Lopes, António M.
2017
Dynamics of the $$N$$-link pendulum: a fractional perspective. Zbl 1417.70005
Lopes, António M.; Tenreiro Machado, J. A.
2017
Solved problems in dynamical systems and control. Zbl 1354.00006
Tenreiro Machado, José; Lopes, António M.; Valério, Duarte; Galhano, Alexandra M.
2017
Generalized two-port elements. Zbl 1473.94169
Tenreiro Machado, J.; Galhano, Alexandra M.
2017
Dynamic stability analysis of fractional order leaky integrator echo state neural networks. Zbl 07257498
Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.
2017
On the mathematical modeling of soccer dynamics. Zbl 07261243
Tenreiro Machado, J. A.; Lopes, António M.
2017
Erratum to: “Some pioneers of the applications of fractional calculus”. Zbl 1473.26003
Valério, Duarte; Tenreiro Machado, José; Kiryakova, Virginia
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
2016
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.
2016
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.
2016
Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. Zbl 1354.35180
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Hristov, Jordan
2016
...and 126 more Documents
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### Cited in 303 Serials

 161 Advances in Difference Equations 156 Nonlinear Dynamics 122 Computational and Applied Mathematics 121 Fractional Calculus & Applied Analysis 111 Communications in Nonlinear Science and Numerical Simulation 108 Applied Mathematics and Computation 97 Abstract and Applied Analysis 85 Chaos, Solitons and Fractals 80 Computers & Mathematics with Applications 62 Mathematical Problems in Engineering 58 Journal of Computational and Applied Mathematics 44 Applied Mathematical Modelling 41 Fractals 39 Applied Numerical Mathematics 30 Advances in Mathematical Physics 29 Journal of Function Spaces 28 Boundary Value Problems 27 Journal of Vibration and Control 27 Discrete Dynamics in Nature and Society 26 Journal of the Franklin Institute 26 International Journal of Nonlinear Sciences and Numerical Simulation 26 Journal of Applied Mathematics and Computing 26 International Journal of Applied and Computational Mathematics 25 Journal of Nonlinear Science and Applications 23 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 22 Mathematics and Computers in Simulation 22 Applied Mathematics Letters 21 Automatica 21 Chaos 21 Asian Journal of Control 19 Journal of Optimization Theory and Applications 19 International Journal of Systems Science. Principles and Applications of Systems and Integration 16 Journal of Computational Physics 16 Signal Processing 16 International Journal of Computer Mathematics 16 Mediterranean Journal of Mathematics 15 Complexity 15 Mathematical Sciences 15 Computational Methods for Differential Equations 15 AIMS Mathematics 14 Physica A 13 Mathematical Methods in the Applied Sciences 13 Numerical Algorithms 12 Journal of Mathematical Physics 12 Discrete and Continuous Dynamical Systems. Series S 11 Journal of Scientific Computing 11 Differential Equations and Dynamical Systems 11 Journal of Inequalities and Applications 11 Journal of Applied Mathematics 11 Entropy 11 International Journal of Differential Equations 10 Nonlinear Analysis. Modelling and Control 9 Circuits, Systems, and Signal Processing 9 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 8 International Journal of Theoretical Physics 8 Journal of Mathematical Analysis and Applications 8 International Journal of Applied Mathematics and Computer Science 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 8 Journal of Applied Analysis and Computation 7 International Journal of Control 7 Fractional Differential Calculus 7 Evolution Equations and Control Theory 7 Journal of Mathematics 6 Meccanica 6 Results in Mathematics 6 Neural Networks 6 Engineering Analysis with Boundary Elements 6 Inverse Problems in Science and Engineering 6 Mathematical Modelling of Natural Phenomena 6 International Journal of Biomathematics 6 Tbilisi Mathematical Journal 6 Journal of Mathematical Extension 6 Journal of Applied Nonlinear Dynamics 6 Mathematics 6 Open Mathematics 6 Communications on Applied Mathematics and Computation 5 Acta Mechanica 5 Physics Letters. A 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Mathematical and Computer Modelling 5 International Journal of Robust and Nonlinear Control 5 European Journal of Control 5 Lobachevskii Journal of Mathematics 5 Mathematical Modelling and Analysis 5 Journal of Function Spaces and Applications 5 Proyecciones 5 S$$\vec{\text{e}}$$MA Journal 4 Reports on Mathematical Physics 4 Journal of Geometry and Physics 4 Calcolo 4 Journal of Differential Equations 4 Stochastic Analysis and Applications 4 Filomat 4 Nonlinear Analysis. Real World Applications 4 Hacettepe Journal of Mathematics and Statistics 4 Fixed Point Theory and Applications 4 Journal of Pseudo-Differential Operators and Applications 3 Applicable Analysis 3 Rocky Mountain Journal of Mathematics 3 Bulletin of the Polish Academy of Sciences. Technical Sciences ...and 203 more Serials
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### Cited in 53 Fields

 1,228 Ordinary differential equations (34-XX) 830 Real functions (26-XX) 620 Numerical analysis (65-XX) 609 Partial differential equations (35-XX) 451 Systems theory; control (93-XX) 205 Operator theory (47-XX) 181 Integral equations (45-XX) 172 Biology and other natural sciences (92-XX) 138 Dynamical systems and ergodic theory (37-XX) 127 Special functions (33-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 93 Information and communication theory, circuits (94-XX) 87 Fluid mechanics (76-XX) 83 Mechanics of particles and systems (70-XX) 75 Probability theory and stochastic processes (60-XX) 73 Mechanics of deformable solids (74-XX) 65 Difference and functional equations (39-XX) 55 Integral transforms, operational calculus (44-XX) 51 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 49 Approximations and expansions (41-XX) 48 Statistical mechanics, structure of matter (82-XX) 42 Operations research, mathematical programming (90-XX) 40 Computer science (68-XX) 33 Statistics (62-XX) 30 Harmonic analysis on Euclidean spaces (42-XX) 29 Measure and integration (28-XX) 27 Optics, electromagnetic theory (78-XX) 24 Quantum theory (81-XX) 20 Classical thermodynamics, heat transfer (80-XX) 14 Number theory (11-XX) 14 Functions of a complex variable (30-XX) 14 Global analysis, analysis on manifolds (58-XX) 14 Geophysics (86-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Functional analysis (46-XX) 10 History and biography (01-XX) 8 Relativity and gravitational theory (83-XX) 6 General and overarching topics; collections (00-XX) 5 Combinatorics (05-XX) 5 Topological groups, Lie groups (22-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Differential geometry (53-XX) 4 Mathematics education (97-XX) 3 Potential theory (31-XX) 3 General topology (54-XX) 3 Astronomy and astrophysics (85-XX) 2 Mathematical logic and foundations (03-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Algebraic topology (55-XX)

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