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## Podlubny, Igor

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 Author ID: podlubny.igor Published as: Podlubny, I.; Podlubny, Igor
 Documents Indexed: 42 Publications since 1992, including 4 Books
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#### Co-Authors

 12 single-authored 16 Chen, Yangquan 8 Vinagre, Blas Manuel 6 Petras, Ivo 4 Li, Yan 3 Skovranek, Tomas 2 Ahn, Hyo-Sung 2 Kiryakova, Virginia S. 2 Magin, Richard Lloyd 2 Sierociuk, Dominik 2 Trymorush, Iryna 2 Vinagre Jara, Blas Manuel 1 Chechkin, Aleksei V. 1 Chen, Wen 1 Datsko, Bohdan 1 Dorcak, Lubomir 1 Dzieliński, Andrzej 1 Feliu, Vicente 1 Gafiychuk, Vasyl V. 1 Ge, Fudong 1 Hernández, Antonio J. 1 Jiao, Zhuang 1 Kassayova, Katarina 1 Kou, Chunhai 1 Li, Changpin 1 Liang, Jinsong 1 López-Bernal, Álvaro 1 Meerschaert, Mark M. 1 O’Leary, Patrick M. 1 Ortigueira, Manuel D. 1 Pavluš, Miron 1 Sarwas, Grzegorz 1 Srivastava, Hari Mohan 1 Tejado, Inés 1 Testi, Luca 1 Torres, Daniel Alexdy 1 Trujillo, Juan J. 1 Verbitsky, Viktor 1 Villalobos, Francisco J. 1 Zhang, Chenghui 1 Zhang, Weiwei 1 Zhao, Daduan
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#### Serials

 11 Fractional Calculus & Applied Analysis 4 Nonlinear Dynamics 2 Automatica 2 Kybernetika 2 Signal Processing 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Communications in Nonlinear Science and Numerical Simulation 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 Applied Mathematics and Computation 1 IEEE Transactions on Automatic Control 1 Applied Mathematics Letters 1 IEEE Transactions on Signal Processing 1 Computational Statistics and Data Analysis 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Integral Transforms and Special Functions 1 Mathematics in Science and Engineering 1 SpringerBriefs in Electrical and Computer Engineering
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#### Fields

 20 Real functions (26-XX) 15 Systems theory; control (93-XX) 10 Ordinary differential equations (34-XX) 7 Numerical analysis (65-XX) 6 Special functions (33-XX) 5 Integral equations (45-XX) 3 History and biography (01-XX) 3 Partial differential equations (35-XX) 3 Mechanics of deformable solids (74-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

32 Publications have been cited 10,470 times in 7,699 Documents Cited by Year
Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Zbl 0924.34008
Podlubny, Igor
1999
Solution of linear fractional differential equations with constant coefficients. Zbl 0918.34010
Podlubny, I.
1995
Fractional-order systems and $$PI^ \lambda D^ \mu$$-controllers. Zbl 1056.93542
Podlubny, Igor
1999
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
1998
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
2009
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Zbl 1189.34015
Li, Yan; Chen, Yangquan; Podlubny, Igor
2010
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
2002
Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. Zbl 1160.65308
Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, Yangquan; Vinagre Jara, Blas M.
2009
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
2002
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
1997
Some approximations of fractional order operators used in control theory and applications. Zbl 1111.93302
Vinagre, B. M.; Podlubny, I.; Hernández, A.; Feliu, V.
2000
Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385
Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor
2006
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
2000
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
2004
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
2011
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
2012
Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Zbl 1123.93074
Ahn, Hyo-Sung; Chen, Yangquan; Podlubny, Igor
2007
Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control. Zbl 1031.93110
Vinagre, B. M.; Petráš, I.; Podlubny, I.; Chen, Y. Q.
2002
Modelling heat transfer in heterogeneous media using fractional calculus. Zbl 1382.80004
Sierociuk, Dominik; Dzieliński, Andrzej; Sarwas, Grzegorz; Petras, Ivo; Podlubny, Igor; Skovranek, Tomas
2013
Matrix approach to discrete fractional calculus. III: Non-equidistant grids, variable step length and distributed orders. Zbl 1339.65094
Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M.; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan
2013
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
2012
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
2015
On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 06663385
Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor
2016
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
2007
Robustness of fractional-order boundary control of time fractional wave equations with delayed boundary measurement using the simple predictor. Zbl 1125.93029
Liang, Jinsong; Zhang, Weiwei; Chen, Yangquan; Podlubny, Igor
2007
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
1997
Orthogonal with non-integrable weight function Jacobi polynomials and their application to singular integral equations in elasticity and heat conduction problems. Zbl 0770.45004
Podlubny, I.
1992
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
2004
Porous functions. Zbl 1434.74038
Podlubny, Igor
2019
Niels Henrik Abel and the birth of fractional calculus. Zbl 1374.26002
Podlubny, Igor; Magin, Richard L.; Trymorush, Iryna
2017
Reply to “Comments on ‘Mittag-Leffler stability of fractional order nonlinear dynamic systems’ [Automatica 45(8) (2009) 1965-1969]”. Zbl 1351.93074
Li, Yan; Chen, YangQuan; Podlubny, Igor
2017
Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems. Zbl 0876.65049
Podlubny, Igor
1996
Porous functions. Zbl 1434.74038
Podlubny, Igor
2019
Niels Henrik Abel and the birth of fractional calculus. Zbl 1374.26002
Podlubny, Igor; Magin, Richard L.; Trymorush, Iryna
2017
Reply to “Comments on ‘Mittag-Leffler stability of fractional order nonlinear dynamic systems’ [Automatica 45(8) (2009) 1965-1969]”. Zbl 1351.93074
Li, Yan; Chen, YangQuan; Podlubny, Igor
2017
On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 06663385
Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor
2016
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
2015
Modelling heat transfer in heterogeneous media using fractional calculus. Zbl 1382.80004
Sierociuk, Dominik; Dzieliński, Andrzej; Sarwas, Grzegorz; Petras, Ivo; Podlubny, Igor; Skovranek, Tomas
2013
Matrix approach to discrete fractional calculus. III: Non-equidistant grids, variable step length and distributed orders. Zbl 1339.65094
Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M.; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan
2013
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
2012
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
2012
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
2011
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Zbl 1189.34015
Li, Yan; Chen, Yangquan; Podlubny, Igor
2010
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
2009
Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. Zbl 1160.65308
Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, Yangquan; Vinagre Jara, Blas M.
2009
Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Zbl 1123.93074
Ahn, Hyo-Sung; Chen, Yangquan; Podlubny, Igor
2007
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
2007
Robustness of fractional-order boundary control of time fractional wave equations with delayed boundary measurement using the simple predictor. Zbl 1125.93029
Liang, Jinsong; Zhang, Weiwei; Chen, Yangquan; Podlubny, Igor
2007
Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385
Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor
2006
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
2004
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
2004
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
2002
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
2002
Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control. Zbl 1031.93110
Vinagre, B. M.; Petráš, I.; Podlubny, I.; Chen, Y. Q.
2002
Some approximations of fractional order operators used in control theory and applications. Zbl 1111.93302
Vinagre, B. M.; Podlubny, I.; Hernández, A.; Feliu, V.
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
2000
Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Zbl 0924.34008
Podlubny, Igor
1999
Fractional-order systems and $$PI^ \lambda D^ \mu$$-controllers. Zbl 1056.93542
Podlubny, Igor
1999
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
1998
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
1997
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
1997
Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems. Zbl 0876.65049
Podlubny, Igor
1996
Solution of linear fractional differential equations with constant coefficients. Zbl 0918.34010
Podlubny, I.
1995
Orthogonal with non-integrable weight function Jacobi polynomials and their application to singular integral equations in elasticity and heat conduction problems. Zbl 0770.45004
Podlubny, I.
1992
all top 5

#### Cited by 7,656 Authors

 456 Advances in Difference Equations 453 Applied Mathematics and Computation 382 Computers & Mathematics with Applications 302 Fractional Calculus & Applied Analysis 287 Nonlinear Dynamics 270 Abstract and Applied Analysis 236 Communications in Nonlinear Science and Numerical Simulation 220 Chaos, Solitons and Fractals 191 Journal of Computational and Applied Mathematics 145 Mathematical Problems in Engineering 144 Journal of Computational Physics 119 Applied Numerical Mathematics 117 Applied Mathematics Letters 104 Applied Mathematical Modelling 97 Journal of the Franklin Institute 95 Journal of Applied Mathematics and Computing 90 Journal of Mathematical Analysis and Applications 89 Boundary Value Problems 86 Computational and Applied Mathematics 85 Journal of Scientific Computing 72 Chaos 71 Numerical Algorithms 68 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 64 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 64 Discrete Dynamics in Nature and Society 64 Mediterranean Journal of Mathematics 63 Advances in Mathematical Physics 62 Physics Letters. A 61 Journal of Mathematical Physics 61 Complexity 56 Fractional Differential Calculus 51 Journal of Nonlinear Science and Applications 49 International Journal of Differential Equations 48 Journal of Function Spaces 48 International Journal of Applied and Computational Mathematics 45 Automatica 43 International Journal of Computer Mathematics 41 Journal of Vibration and Control 39 Journal of Applied Mathematics 39 Journal of Applied Analysis and Computation 38 International Journal of Nonlinear Sciences and Numerical Simulation 38 Nonlinear Analysis. Real World Applications 37 Differential Equations and Dynamical Systems 36 Mathematics and Computers in Simulation 34 International Journal of Applied Mathematics and Computer Science 34 Asian Journal of Control 31 SIAM Journal on Scientific Computing 30 Journal of Optimization Theory and Applications 30 Nonlinear Analysis. Modelling and Control 29 Physica A 27 Neural Networks 27 International Journal of Biomathematics 25 Signal Processing 25 Engineering Analysis with Boundary Elements 24 Journal of Integral Equations and Applications 24 Mathematical Modelling of Natural Phenomena 23 Mathematical and Computer Modelling 23 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 23 Open Mathematics 22 International Journal of Modern Physics B 22 Mathematical Methods in the Applied Sciences 22 Circuits, Systems, and Signal Processing 20 Acta Mechanica 20 Journal of Statistical Physics 20 Integral Transforms and Special Functions 20 Mathematical Sciences 20 Mathematics 20 International Journal of Systems Science. Principles and Applications of Systems and Integration 19 International Journal of Control 19 Fractals 19 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 18 SIAM Journal on Numerical Analysis 18 Tbilisi Mathematical Journal 17 International Journal of Theoretical Physics 17 Numerical Functional Analysis and Optimization 17 Cybernetics and Systems Analysis 17 Journal of the Egyptian Mathematical Society 17 Acta Mechanica Sinica 17 Discrete and Continuous Dynamical Systems. Series S 16 Applicable Analysis 16 Computer Methods in Applied Mechanics and Engineering 16 Results in Mathematics 16 Advances in Computational Mathematics 16 Symmetry 16 S$$\vec{\text{e}}$$MA Journal 15 Journal of Mathematics 14 Reports on Mathematical Physics 14 Stochastic Analysis and Applications 14 International Journal of Numerical Methods for Heat & Fluid Flow 14 Journal of Inequalities and Applications 14 Axioms 13 Rocky Mountain Journal of Mathematics 13 SIAM Journal on Control and Optimization 13 Systems & Control Letters 13 Turkish Journal of Mathematics 13 Discrete and Continuous Dynamical Systems. Series B 13 Boletim da Sociedade Paranaense de Matemática. Terceira Série 13 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 12 Acta Applicandae Mathematicae 12 Differential Equations ...and 368 more Serials