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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

38 Publications have been cited 15,858 times in 13,527 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.
771
1998
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
549
2009
Fractional-order systems and \(PI^ \lambda D^ \mu\)-controllers. Zbl 1056.93542
Podlubny, Igor
529
1999
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Zbl 1189.34015
Li, Yan; Chen, Yangquan; Podlubny, Igor
505
2010
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
383
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.
178
2009
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
155
1997
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
125
2002
Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005
Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor
118
2012
Some approximations of fractional order operators used in control theory and applications. Zbl 1111.93302
Vinagre, B. M.; Podlubny, I.; Hernández, A.; Feliu, V.
110
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
93
2000
Modelling heat transfer in heterogeneous media using fractional calculus. Zbl 1382.80004
Sierociuk, Dominik; Dzieliński, Andrzej; Sarwas, Grzegorz; Petras, Ivo; Podlubny, Igor; Skovranek, Tomas
74
2013
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
73
2011
Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385
Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor
67
2006
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
61
2007
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
61
2004
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.
56
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
41
2013
Finite energy Lyapunov function candidate for fractional order general nonlinear systems. Zbl 1479.34121
Li, Yan; Zhao, Daduan; Chen, YangQuan; Podlubny, Igor; Zhang, Chenghui
15
2019
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
14
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
13
2016
Niels Henrik Abel and the birth of fractional calculus. Zbl 1374.26002
Podlubny, Igor; Magin, Richard L.; Trymorush, Iryna
12
2017
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
11
2015
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.
5
1992
State space description of national economies: the V4 countries. Zbl 1452.62955
Petras, Ivo; Podlubny, Igor
5
2007
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
5
1997
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
5
2004
Monte Carlo method for fractional-order differentiation extended to higher orders. Zbl 1503.65046
Leonenko, Nikolai; Podlubny, Igor
4
2022
Monte Carlo method for fractional-order differentiation. Zbl 1503.65047
Leonenko, Nikolai; Podlubny, Igor
3
2022
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
Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems. Zbl 0876.65049
Podlubny, Igor
1
1996
Parallel method for initial value problems for linear ordinary differential equations: Speed up estimation. Zbl 0916.65077
Pavluš, Miron; Podlubny, Igor
1
1997
Fractional approach for estimating sap velocity in trees. Zbl 1327.80008
Tejado, Inés; Vinagre, Blas M.; Torres, Daniel; López-Bernal, Álvaro; Villalobos, Francisco J.; Testi, Luca; Podlubny, Igor
1
2015
Editorial: FCAA related meetings and news (FCAA-volume 16-1-2013). Zbl 1315.00104
1
2013
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
Porous functions. Zbl 1434.74038
Podlubny, Igor
1
2019
Monte Carlo method for fractional-order differentiation extended to higher orders. Zbl 1503.65046
Leonenko, Nikolai; Podlubny, Igor
4
2022
Monte Carlo method for fractional-order differentiation. Zbl 1503.65047
Leonenko, Nikolai; Podlubny, Igor
3
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
15
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
12
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
13
2016
Solitary travelling auto-waves in fractional reaction-diffusion systems. Zbl 1440.35341
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
11
2015
Fractional approach for estimating sap velocity in trees. Zbl 1327.80008
Tejado, Inés; Vinagre, Blas M.; Torres, Daniel; López-Bernal, Álvaro; Villalobos, Francisco J.; Testi, Luca; Podlubny, Igor
1
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
74
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
41
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
118
2012
Identification of parameters of a half-order system. Zbl 1393.94966
Petráš, Ivo; Sierociuk, Dominik; Podlubny, Igor
14
2012
On the fractional signals and systems. Zbl 1203.94041
Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan
73
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
505
2010
Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
549
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.
178
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
61
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
67
2006
Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
61
2004
Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334
Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor
5
2004
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
383
2002
Anlogue realizations of fractional-order controllers. Zbl 1041.93022
Podlubny, I.; Petráš, I.; Vinagre, B. M.; O’Leary, P.; Dorčák, L’.
125
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.
56
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.
110
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
93
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
529
1999
Application of orthogonal polynomials to solution of fractional integral equations. Zbl 0922.45001
Podlubny, I.
771
1998
Numerical solution of ordinary fractional differential equations by the fractional difference method. Zbl 0893.65051
Podlubny, I.
155
1997
Riesz potential and Riemann-Liouville fractional integrals and derivatives of Jacobi polynomials. Zbl 0883.33003
Podlubny, I.
5
1997
Parallel method for initial value problems for linear ordinary differential equations: Speed up estimation. Zbl 0916.65077
Pavluš, Miron; Podlubny, Igor
1
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.
5
1992
all top 5

Cited by 11,866 Authors

411 Băleanu, Dumitru I.
164 Abdeljawad, Thabet
137 Liu, Fawang
133 Ntouyas, Sotiris K.
128 Ahmad, Bashir
122 Shah, Kamal
121 Cao, Jinde
109 Machado, José António Tenreiro
108 Zhou, Yong
98 Chen, Yangquan
97 Wang, Hong
91 Agarwal, Ravi P.
91 Nieto Roig, Juan Jose
85 Al-saedi, Ahmed Eid Salem
85 Momani, Shaher M.
84 Rezapour, Shahram
80 Wang, Jinrong
77 Sooppy Nisar, Kottakkaran
74 Jarad, Fahd
73 Gómez-Aguilar, José Francisco
73 Turner, Ian William
72 Benchohra, Mouffak
71 Li, Changpin
67 Atangana, Abdon
65 Deng, Weihua
65 O’Regan, Donal
63 Liu, Lishan
61 Tariboon, Jessada
60 Srivastava, Hari Mohan
59 Anh, Vo V.
59 Jafari, Hossein
58 Heydari, Mohammad Hossein
57 Tarasov, Vasily E.
56 Zada, Akbar
55 Owolabi, Kolade Matthew
54 Nguyen Huy Tuan
51 Wu, Yonghong
49 Khan, Rahmat Ali
49 Sun, Haiwei
48 Alzabut, Jehad O.
48 Jiang, Xiaoyun
48 Vijayakumar, Velusamy
47 Kumar, Sunil
47 Zheng, Xiangcheng
46 Odibat, Zaid M.
45 Huang, Chengdai
45 Torres, Delfim Fernando Marado
43 Khan, Aziz Ullah
42 Kumar, Devendra
42 Sun, Zhizhong
41 Daftardar-Gejji, Varsha
40 Etemad, Sina
40 Kaczorek, Tadeusz
40 Trujillo, Juan J.
39 Jiang, Wei
39 Xu, Da
38 Avazzadeh, Zakieh
38 Singh, Jagdev
38 Tavazoei, Mohammad Saleh
38 Yamamoto, Masahiro
38 Yu, Yongguang
37 Veeresha, Pundikala
36 Wei, Ting
35 Abdo, Mohammed Salem
35 Balachandran, Krishnan
35 Ibrahim, Rabha Waell
35 Inc, Mustafa
35 Tatar, Nasser-eddine
34 Dehghan Takht Fooladi, Mehdi
34 Khan, Hasib
34 Pandey, Dwijendra Narain
34 Wu, Ranchao
33 Chen, Wen
33 Liu, Zhenhai
33 Qiu, Wenlin
32 El-Sayed, Ahmed Mohamed Ahmed
32 Karniadakis, George Em
32 Sun, Hongguang
32 Sweilam, Nasser Hassan
32 Wang, Guotao
32 Wu, Guocheng
31 Garrappa, Roberto
31 Khader, Mohamed M.
31 Mainardi, Francesco
31 Salahshour, Soheil
31 Zheng, Liancun
30 Agarwal, Praveen
30 Ardjouni, Abdelouaheb
30 Chu, Yuming
30 Henderson, Johnny Lee
30 Khristova, Snezhana G.
30 Sun, Shurong
30 Zaky, Mahmoud A.
29 Abbas, Said
29 Ben Makhlouf, Abdellatif
29 Mahmudov, Nazim Idrisoglu
29 Rashid, Saima
29 Saha Ray, Santanu
29 Udhayakumar, Ramalingam
29 Zeng, Fanhai
...and 11,766 more Authors
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Cited in 611 Serials

788 Advances in Difference Equations
541 Applied Mathematics and Computation
506 Mathematical Methods in the Applied Sciences
463 Computers & Mathematics with Applications
462 Fractional Calculus & Applied Analysis
460 Chaos, Solitons and Fractals
407 Communications in Nonlinear Science and Numerical Simulation
316 Nonlinear Dynamics
313 Abstract and Applied Analysis
250 Journal of Computational and Applied Mathematics
183 Mathematical Problems in Engineering
181 Computational and Applied Mathematics
172 Applied Numerical Mathematics
170 Boundary Value Problems
155 Applied Mathematical Modelling
152 Journal of Computational Physics
152 Mathematics and Computers in Simulation
151 Fractals
149 Journal of Function Spaces
148 Applied Mathematics Letters
145 Journal of Applied Mathematics and Computing
142 Physica A
141 Journal of the Franklin Institute
132 Numerical Methods for Partial Differential Equations
131 International Journal of Computer Mathematics
130 Journal of Scientific Computing
118 International Journal of Applied and Computational Mathematics
115 Advances in Mathematical Physics
114 AIMS Mathematics
113 Numerical Algorithms
103 International Journal of Nonlinear Sciences and Numerical Simulation
99 Journal of Mathematical Analysis and Applications
94 Discrete Dynamics in Nature and Society
89 Fractional Differential Calculus
85 Mediterranean Journal of Mathematics
81 Chaos
79 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
78 Complexity
72 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
72 International Journal of Systems Science. Principles and Applications of Systems and Integration
69 International Journal of Differential Equations
68 Nonlinear Analysis. Modelling and Control
67 Asian Journal of Control
66 Journal of Mathematical Physics
66 Physics Letters. A
64 Filomat
64 Journal of Inequalities and Applications
62 Neural Networks
56 Computational Methods for Differential Equations
55 Discrete and Continuous Dynamical Systems. Series S
53 Differential Equations and Dynamical Systems
52 Journal of Nonlinear Science and Applications
51 Qualitative Theory of Dynamical Systems
51 Journal of Applied Mathematics
48 Automatica
47 Journal of Applied Analysis and Computation
46 Mathematical Sciences
45 Chinese Journal of Physics (Taipei)
42 International Journal of Biomathematics
41 Journal of Vibration and Control
40 Engineering Analysis with Boundary Elements
39 International Journal of Applied Mathematics and Computer Science
38 Nonlinear Analysis. Real World Applications
37 International Journal of Robust and Nonlinear Control
37 SIAM Journal on Scientific Computing
37 Open Mathematics
36 Journal of Mathematics
34 Journal of Optimization Theory and Applications
34 Journal of Applied Nonlinear Dynamics
33 Journal of Integral Equations and Applications
33 Turkish Journal of Mathematics
32 Applicable Analysis
32 Circuits, Systems, and Signal Processing
32 Journal of Mathematical Extension
29 Waves in Random and Complex Media
29 Mathematical Modelling of Natural Phenomena
27 Acta Mechanica
27 Rocky Mountain Journal of Mathematics
27 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
27 Journal of Statistical Mechanics: Theory and Experiment
27 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
26 Inverse Problems
26 Boletim da Sociedade Paranaense de Matemática. Terceira Série
26 Tbilisi Mathematical Journal
25 Signal Processing
24 Numerical Functional Analysis and Optimization
24 Mathematical and Computer Modelling
24 Inverse Problems in Science and Engineering
24 S\(\vec{\text{e}}\)MA Journal
23 Journal of Statistical Physics
23 Meccanica
23 SIAM Journal on Numerical Analysis
23 Integral Transforms and Special Functions
23 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis
23 Asian-European Journal of Mathematics
23 Advances in Applied Mathematics and Mechanics
22 International Journal of Modern Physics B
22 Reports on Mathematical Physics
22 Advances in Computational Mathematics
22 Applied Mathematics E-Notes
...and 511 more Serials
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Cited in 57 Fields

6,300 Ordinary differential equations (34-XX)
4,324 Real functions (26-XX)
4,172 Partial differential equations (35-XX)
3,649 Numerical analysis (65-XX)
1,949 Systems theory; control (93-XX)
1,522 Operator theory (47-XX)
996 Integral equations (45-XX)
925 Biology and other natural sciences (92-XX)
594 Special functions (33-XX)
545 Probability theory and stochastic processes (60-XX)
524 Dynamical systems and ergodic theory (37-XX)
492 Fluid mechanics (76-XX)
397 Calculus of variations and optimal control; optimization (49-XX)
371 Mechanics of deformable solids (74-XX)
321 Difference and functional equations (39-XX)
316 Integral transforms, operational calculus (44-XX)
296 Statistical mechanics, structure of matter (82-XX)
204 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
203 Information and communication theory, circuits (94-XX)
178 Mechanics of particles and systems (70-XX)
148 Approximations and expansions (41-XX)
138 Classical thermodynamics, heat transfer (80-XX)
129 Computer science (68-XX)
123 Quantum theory (81-XX)
120 Harmonic analysis on Euclidean spaces (42-XX)
96 Global analysis, analysis on manifolds (58-XX)
85 Measure and integration (28-XX)
79 Operations research, mathematical programming (90-XX)
73 Functional analysis (46-XX)
68 Linear and multilinear algebra; matrix theory (15-XX)
64 Functions of a complex variable (30-XX)
64 Optics, electromagnetic theory (78-XX)
46 Statistics (62-XX)
37 Number theory (11-XX)
36 Combinatorics (05-XX)
36 Geophysics (86-XX)
33 Relativity and gravitational theory (83-XX)
27 General topology (54-XX)
18 Abstract harmonic analysis (43-XX)
17 Differential geometry (53-XX)
12 Topological groups, Lie groups (22-XX)
12 Potential theory (31-XX)
11 History and biography (01-XX)
11 Sequences, series, summability (40-XX)
9 Several complex variables and analytic spaces (32-XX)
8 General and overarching topics; collections (00-XX)
5 Nonassociative rings and algebras (17-XX)
5 Mathematics education (97-XX)
4 Algebraic topology (55-XX)
4 Astronomy and astrophysics (85-XX)
3 Mathematical logic and foundations (03-XX)
2 Algebraic geometry (14-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