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Author ID: podlubny.igor Recent zbMATH articles by "Podlubny, Igor"
Published as: Podlubny, Igor; Podlubny, I.
Homepage: http://people.tuke.sk/igor.podlubny/
External Links: ORCID · Google Scholar · dblp

Publications by Year

Citations contained in zbMATH Open

35 Publications have been cited 12,354 times in 10,503 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
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
633
1998
Fractional-order systems and \(PI^ \lambda D^ \mu\)-controllers. Zbl 1056.93542
Podlubny, Igor
460
1999
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
449
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
418
2010
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
334
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.
162
2009
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
145
1997
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
112
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.
91
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
79
2000
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
66
2012
Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385
Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor
62
2006
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
61
2011
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
59
2004
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
54
2007
Modelling heat transfer in heterogeneous media using fractional calculus. Zbl 1382.80004
Sierociuk, Dominik; Dzieliński, Andrzej; Sarwas, Grzegorz; Petras, Ivo; Podlubny, Igor; Skovranek, Tomas
53
2013
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.
48
2002
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
34
2013
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
11
2015
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
11
2012
On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 1499.93010
Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor
9
2016
Niels Henrik Abel and the birth of fractional calculus. Zbl 1374.26002
Podlubny, Igor; Magin, Richard L.; Trymorush, Iryna
8
2017
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
5
2007
Finite energy Lyapunov function candidate for fractional order general nonlinear systems. Zbl 1479.34121
Li, Yan; Zhao, Daduan; Chen, YangQuan; Podlubny, Igor; Zhang, Chenghui
5
2019
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
4
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.
4
1992
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
3
2004
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
3
2007
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
1
2017
Editorial: FCAA related meetings and news (FCAA-volume 16-1-2013). Zbl 1315.00104
1
2013
Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems. Zbl 0876.65049
Podlubny, Igor
1
1996
Porous functions. Zbl 1434.74038
Podlubny, Igor
1
2019
Monte Carlo method for fractional-order differentiation. Zbl 1503.65047
Leonenko, Nikolai; Podlubny, Igor
1
2022
Monte Carlo method for fractional-order differentiation. Zbl 1503.65047
Leonenko, Nikolai; Podlubny, Igor
1
2022
Finite energy Lyapunov function candidate for fractional order general nonlinear systems. Zbl 1479.34121
Li, Yan; Zhao, Daduan; Chen, YangQuan; Podlubny, Igor; Zhang, Chenghui
5
2019
Porous functions. Zbl 1434.74038
Podlubny, Igor
1
2019
Niels Henrik Abel and the birth of fractional calculus. Zbl 1374.26002
Podlubny, Igor; Magin, Richard L.; Trymorush, Iryna
8
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
1
2017
On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 1499.93010
Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor
9
2016
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
11
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
53
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
34
2013
Editorial: FCAA related meetings and news (FCAA-volume 16-1-2013). Zbl 1315.00104
1
2013
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
66
2012
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
11
2012
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
61
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
418
2010
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
449
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.
162
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
54
2007
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
5
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
3
2007
Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385
Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor
62
2006
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
59
2004
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
3
2004
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
334
2002
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
112
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.
48
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.
91
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
79
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
460
1999
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
633
1998
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
145
1997
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
4
1997
Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems. Zbl 0876.65049
Podlubny, Igor
1
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.
4
1992
all top 5

Cited by 9,801 Authors

346 Băleanu, Dumitru I.
129 Abdeljawad, Thabet
123 Ntouyas, Sotiris K.
116 Liu, Fawang
114 Ahmad, Bashir
93 Machado, José António Tenreiro
90 Cao, Jinde
83 Chen, Yangquan
82 Wang, Hong
80 Shah, Kamal
79 Agarwal, Ravi P.
76 Momani, Shaher M.
72 Wang, Jinrong
70 Nieto Roig, Juan Jose
70 Rezapour, Shahram
68 Al-saedi, Ahmed Eid Salem
66 Turner, Ian William
64 Li, Changpin
63 Jarad, Fahd
62 Benchohra, Mouffak
59 O’Regan, Donal
59 Tariboon, Jessada
57 Zhou, Yong
54 Atangana, Abdon
54 Gómez-Aguilar, José Francisco
52 Tarasov, Vasily E.
51 Anh, Vo V.
51 Deng, Weihua
51 Jafari, Hossein
51 Liu, Lishan
49 Owolabi, Kolade Matthew
47 Sooppy Nisar, Kottakkaran
47 Srivastava, Hari Mohan
42 Odibat, Zaid M.
41 Daftardar-Gejji, Varsha
39 Heydari, Mohammad Hossien
38 Khan, Rahmat Ali
38 Sun, Zhizhong
38 Trujillo, Juan J.
38 Wu, Yonghong
37 Alzabut, Jehad O.
37 Nguyen Huy Tuan
37 Sun, Haiwei
37 Torres, Delfim Fernando Marado
37 Zheng, Xiangcheng
36 Jiang, Xiaoyun
35 Etemad, Sina
35 Huang, Chengdai
34 Jiang, Wei
34 Zada, Akbar
33 Balachandran, Krishnan
33 Ibrahim, Rabha Waell
33 Tavazoei, Mohammad Saleh
32 Kaczorek, Tadeusz
32 Khan, Aziz
31 Kumar, Sunil
30 Singh, Jagdev
29 Abdo, Mohammed Salem
29 El-Sayed, Ahmed Mohamed Ahmed
29 Khristova, Snezhana G.
29 Wu, Ranchao
29 Xu, Da
29 Yu, Yongguang
28 Karniadakis, George Em
28 Kumar, Devendra
28 Mainardi, Francesco
27 Chu, Yuming
27 Henderson, Johnny Lee
27 Inc, Mustafa
27 Khader, Mohamed M.
27 Sun, Hongguang
27 Wang, Guotao
27 Wu, Guocheng
26 Avazzadeh, Zakieh
26 Khan, Hasib
26 Liu, Zhenhai
26 Povstenko, Yuriy Z.
25 Ardjouni, Abdelouaheb
25 Pandey, Dwijendra Narain
25 Sweilam, Nasser Hassan
25 Zeng, Fanhai
25 Zheng, Liancun
24 Mahmudov, Nazim Idrisoglu
24 Tatar, Nasser-eddine
23 Abbas, Said
23 Bhalekar, Sachin
23 Fečkan, Michal
23 Hammouch, Zakia
23 Kiliçman, Adem
23 Meerschaert, Mark Marvin
23 Vijayakumar, Velusamy
23 Wei, Ting
23 Yamamoto, Masahiro
23 Zhou, Yong
22 Chen, Liping
22 Chen, Wen
22 Haeri, Mohammad
22 Wang, Yong
22 Yang, Xiao-Jun
21 Agrawal, Om Prakash
...and 9,701 more Authors
all top 5

Cited in 551 Serials

733 Advances in Difference Equations
492 Applied Mathematics and Computation
423 Chaos, Solitons and Fractals
380 Computers & Mathematics with Applications
369 Fractional Calculus & Applied Analysis
287 Nonlinear Dynamics
287 Communications in Nonlinear Science and Numerical Simulation
261 Abstract and Applied Analysis
209 Journal of Computational and Applied Mathematics
156 Applied Numerical Mathematics
153 Boundary Value Problems
147 Journal of Computational Physics
147 Computational and Applied Mathematics
144 Mathematical Problems in Engineering
137 Journal of Applied Mathematics and Computing
130 Journal of the Franklin Institute
129 Fractals
126 Physica A
121 Applied Mathematics Letters
120 Applied Mathematical Modelling
116 Journal of Function Spaces
113 International Journal of Applied and Computational Mathematics
109 Journal of Scientific Computing
102 Advances in Mathematical Physics
101 International Journal of Computer Mathematics
99 AIMS Mathematics
97 Numerical Algorithms
91 Mathematics and Computers in Simulation
88 Journal of Mathematical Analysis and Applications
78 Mediterranean Journal of Mathematics
77 Discrete Dynamics in Nature and Society
74 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
73 Chaos
69 Fractional Differential Calculus
65 Physics Letters. A
64 Journal of Mathematical Physics
61 Complexity
61 International Journal of Nonlinear Sciences and Numerical Simulation
60 International Journal of Differential Equations
58 Filomat
58 International Journal of Systems Science. Principles and Applications of Systems and Integration
51 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
51 Journal of Inequalities and Applications
51 Journal of Nonlinear Science and Applications
47 Differential Equations and Dynamical Systems
46 Automatica
45 Nonlinear Analysis. Modelling and Control
42 Journal of Applied Mathematics
42 Journal of Applied Analysis and Computation
42 Computational Methods for Differential Equations
41 Journal of Vibration and Control
39 International Journal of Applied Mathematics and Computer Science
35 Open Mathematics
34 International Journal of Biomathematics
34 Asian Journal of Control
33 Nonlinear Analysis. Real World Applications
33 Journal of Applied Nonlinear Dynamics
32 Journal of Optimization Theory and Applications
32 SIAM Journal on Scientific Computing
32 Journal of Mathematics
31 Neural Networks
30 Circuits, Systems, and Signal Processing
29 Engineering Analysis with Boundary Elements
29 Mathematical Sciences
28 Mathematical Modelling of Natural Phenomena
28 Journal of Mathematical Extension
27 Acta Mechanica
27 Applicable Analysis
26 Discrete and Continuous Dynamical Systems. Series S
25 Signal Processing
25 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
25 Waves in Random and Complex Media
25 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
24 Journal of Integral Equations and Applications
24 Turkish Journal of Mathematics
24 Tbilisi Mathematical Journal
24 S\(\vec{\text{e}}\)MA Journal
23 Journal of Statistical Physics
23 Advances in Applied Mathematics and Mechanics
22 International Journal of Modern Physics B
22 Mathematical Methods in the Applied Sciences
21 Integral Transforms and Special Functions
20 SIAM Journal on Numerical Analysis
20 Mathematical and Computer Modelling
20 Mathematics
19 International Journal of Control
19 Reports on Mathematical Physics
19 Cybernetics and Systems Analysis
19 Advances in Computational Mathematics
19 Inverse Problems in Science and Engineering
19 Asian-European Journal of Mathematics
18 Numerical Functional Analysis and Optimization
18 Results in Mathematics
18 Stochastic Analysis and Applications
18 Qualitative Theory of Dynamical Systems
18 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis
17 Computer Methods in Applied Mechanics and Engineering
17 International Journal of Theoretical Physics
17 Journal of the Egyptian Mathematical Society
17 Soft Computing
...and 451 more Serials
all top 5

Cited in 56 Fields

4,923 Ordinary differential equations (34-XX)
3,399 Real functions (26-XX)
3,136 Partial differential equations (35-XX)
2,796 Numerical analysis (65-XX)
1,498 Systems theory; control (93-XX)
1,145 Operator theory (47-XX)
779 Integral equations (45-XX)
683 Biology and other natural sciences (92-XX)
440 Special functions (33-XX)
430 Dynamical systems and ergodic theory (37-XX)
405 Probability theory and stochastic processes (60-XX)
381 Fluid mechanics (76-XX)
293 Calculus of variations and optimal control; optimization (49-XX)
293 Mechanics of deformable solids (74-XX)
260 Statistical mechanics, structure of matter (82-XX)
237 Difference and functional equations (39-XX)
235 Integral transforms, operational calculus (44-XX)
174 Information and communication theory, circuits (94-XX)
155 Mechanics of particles and systems (70-XX)
151 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
108 Classical thermodynamics, heat transfer (80-XX)
106 Quantum theory (81-XX)
104 Approximations and expansions (41-XX)
99 Computer science (68-XX)
86 Harmonic analysis on Euclidean spaces (42-XX)
77 Global analysis, analysis on manifolds (58-XX)
67 Measure and integration (28-XX)
67 Operations research, mathematical programming (90-XX)
56 Linear and multilinear algebra; matrix theory (15-XX)
55 Optics, electromagnetic theory (78-XX)
53 Functional analysis (46-XX)
51 Functions of a complex variable (30-XX)
38 Statistics (62-XX)
33 Geophysics (86-XX)
31 Combinatorics (05-XX)
28 Relativity and gravitational theory (83-XX)
24 Number theory (11-XX)
23 General topology (54-XX)
16 Abstract harmonic analysis (43-XX)
12 Potential theory (31-XX)
11 History and biography (01-XX)
11 Differential geometry (53-XX)
10 Topological groups, Lie groups (22-XX)
8 General and overarching topics; collections (00-XX)
8 Mathematics education (97-XX)
6 Several complex variables and analytic spaces (32-XX)
6 Sequences, series, summability (40-XX)
4 Astronomy and astrophysics (85-XX)
3 Mathematical logic and foundations (03-XX)
3 Nonassociative rings and algebras (17-XX)
3 Algebraic topology (55-XX)
2 Convex and discrete geometry (52-XX)
1 Field theory and polynomials (12-XX)
1 Commutative algebra (13-XX)
1 Category theory; homological algebra (18-XX)
1 Group theory and generalizations (20-XX)

Citations by Year