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Podlubny, Igor

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Author ID: podlubny.igor Recent zbMATH articles by "Podlubny, Igor"
Published as: Podlubny, I.; Podlubny, Igor
Documents Indexed: 42 Publications since 1992, including 4 Books

Publications by Year

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
419
1999
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
348
1998
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
321
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
292
2010
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
264
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.
139
2009
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
104
2002
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
91
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.
81
2000
Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385
Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor
64
2006
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
64
2000
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
55
2004
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
49
2011
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
48
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
48
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.
45
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
40
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
26
2013
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
10
2012
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
8
2015
On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 06663385
Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor
6
2016
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
4
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
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
3
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.
3
1992
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
2
2004
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
1
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
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
Niels Henrik Abel and the birth of fractional calculus. Zbl 1374.26002
Podlubny, Igor; Magin, Richard L.; Trymorush, Iryna
1
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 06663385
Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor
6
2016
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
8
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
40
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
26
2013
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
48
2012
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
10
2012
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
49
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
292
2010
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
321
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.
139
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
48
2007
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
4
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
64
2006
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
55
2004
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
2
2004
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
264
2002
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
104
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.
45
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.
81
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
64
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
419
1999
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
348
1998
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
91
1997
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
3
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.
3
1992
all top 5

Cited by 7,656 Authors

261 Băleanu, Dumitru I.
107 Liu, Fawang
100 Ntouyas, Sotiris K.
98 Ahmad, Bashir
87 Machado, José António Tenreiro
82 Chen, Yangquan
72 Wang, Jinrong
67 Momani, Shaher M.
63 Agarwal, Ravi P.
62 Turner, Ian William
59 Li, Changpin
59 Nieto Roig, Juan Jose
59 Zhou, Yong
58 Abdeljawad, Thabet
58 Cao, Jinde
58 Wang, Hong
57 Al-saedi, Ahmed Eid Salem
53 Benchohra, Mouffak
51 Liu, Lishan
48 Tariboon, Jessada
44 Anh, Vo V.
44 Tarasov, Vasily E.
43 Atangana, Abdon
43 Srivastava, Hari Mohan
42 Deng, Weihua
42 O’Regan, Donal
41 Odibat, Zaid M.
40 Daftardar-Gejji, Varsha
39 Wu, Yonghong
37 Shah, Kamal
36 Jafari, Hossein
35 Sun, Zhizhong
35 Trujillo, Juan J.
34 Khan, Rahmat Ali
34 Torres, Delfim Fernando Marado
33 Jarad, Fahd
32 Gómez-Aguilar, José Francisco
32 Ibrahim, Rabha Waell
31 Tavazoei, Mohammad Saleh
30 Jiang, Xiaoyun
29 Karniadakis, George Em
29 Owolabi, Kolade Matthew
28 Jiang, Wei
27 El-Sayed, Ahmed Mohamed Ahmed
27 Mainardi, Francesco
27 Wu, Ranchao
26 Kaczorek, Tadeusz
26 Nguyen Huy Tuan
26 Wang, Guotao
25 Balachandran, Krishnan
25 Chen, Wen
25 Povstenko, Yuriy Z.
24 Henderson, Johnny Lee
24 Pandey, Dwijendra Narain
24 Tatar, Nasser-eddine
23 Abbas, Said
23 Meerschaert, Mark M.
23 Zhang, Xinguang
23 Zheng, Liancun
22 Bhrawy, Ali Hassan
22 Haeri, Mohammad
22 Khader, Mohamed M.
22 Liu, Zhenhai
22 Sun, Shurong
21 Bettayeb, Maamar
21 Bhalekar, Sachin
21 Garrappa, Roberto
21 Han, Zhenlai
21 Kiliçman, Adem
21 Wang, Zhen
21 Wu, Guocheng
20 Atanackovic, Teodor M.
20 Burrage, Kevin
20 Chen, Liping
20 Debbouche, Amar
20 Fečkan, Michal
20 Heydari, Mohammad Hossien
20 Liu, Yuji
20 Lopes, António M.
20 Sun, Haiwei
20 Sun, Hongguang
20 Wang, Yong
20 Yu, Yongguang
20 Zeng, Fanhai
19 Agrawal, Om Prakash
19 Gorenflo, Rudolf
19 Huang, Chengdai
19 Nyamoradi, Nemat
19 Saha Ray, Santanu
19 Wei, Ting
18 Graef, John R.
18 Khristova, Snezhana G.
18 Podlubny, Igor
18 Singh, Jagdev
18 Sweilam, Nasser Hassan
18 Wei, Yiheng
18 Yang, Xiao-Jun
18 Zheng, Xiangcheng
17 Almeida, Ricardo
17 Bulavatskyĭ, Volodymyr M.
...and 7,556 more Authors
all top 5

Cited in 468 Serials

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
all top 5

Cited in 56 Fields

3,617 Ordinary differential equations (34-XX)
2,292 Partial differential equations (35-XX)
2,222 Real functions (26-XX)
2,042 Numerical analysis (65-XX)
1,135 Systems theory; control (93-XX)
714 Operator theory (47-XX)
640 Integral equations (45-XX)
372 Biology and other natural sciences (92-XX)
342 Dynamical systems and ergodic theory (37-XX)
335 Special functions (33-XX)
304 Fluid mechanics (76-XX)
287 Probability theory and stochastic processes (60-XX)
242 Calculus of variations and optimal control; optimization (49-XX)
226 Mechanics of deformable solids (74-XX)
161 Difference and functional equations (39-XX)
156 Integral transforms, operational calculus (44-XX)
145 Information and communication theory, circuits (94-XX)
141 Statistical mechanics, structure of matter (82-XX)
131 Mechanics of particles and systems (70-XX)
96 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
91 Classical thermodynamics, heat transfer (80-XX)
88 Quantum theory (81-XX)
86 Approximations and expansions (41-XX)
81 Computer science (68-XX)
59 Harmonic analysis on Euclidean spaces (42-XX)
59 Global analysis, analysis on manifolds (58-XX)
53 Operations research, mathematical programming (90-XX)
42 Measure and integration (28-XX)
39 Functions of a complex variable (30-XX)
38 Linear and multilinear algebra; matrix theory (15-XX)
37 Optics, electromagnetic theory (78-XX)
34 Functional analysis (46-XX)
33 Statistics (62-XX)
27 Relativity and gravitational theory (83-XX)
26 Geophysics (86-XX)
21 Combinatorics (05-XX)
19 Number theory (11-XX)
17 Abstract harmonic analysis (43-XX)
13 General topology (54-XX)
11 General and overarching topics; collections (00-XX)
10 History and biography (01-XX)
10 Differential geometry (53-XX)
7 Topological groups, Lie groups (22-XX)
7 Potential theory (31-XX)
6 Several complex variables and analytic spaces (32-XX)
5 Sequences, series, summability (40-XX)
5 Mathematics education (97-XX)
3 Algebraic topology (55-XX)
3 Astronomy and astrophysics (85-XX)
2 Nonassociative rings and algebras (17-XX)
2 Group theory and generalizations (20-XX)
2 Convex and discrete geometry (52-XX)
1 Mathematical logic and foundations (03-XX)
1 Field theory and polynomials (12-XX)
1 Associative rings and algebras (16-XX)
1 Manifolds and cell complexes (57-XX)

Citations by Year