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Author ID: garrappa.roberto Recent zbMATH articles by "Garrappa, Roberto"
Published as: Garrappa, Roberto

Publications by Year

Citations contained in zbMATH Open

46 Publications have been cited 1,116 times in 742 Documents Cited by Year
Numerical solution of fractional differential equations: a survey and a software tutorial. Zbl 06916890
Garrappa, Roberto
97
2018
Numerical evaluation of two and three parameter Mittag-Leffler functions. Zbl 1331.33043
Garrappa, Roberto
89
2015
On linear stability of predictor-corrector algorithms for fractional differential equations. Zbl 1206.65197
Garrappa, Roberto
83
2010
Trapezoidal methods for fractional differential equations: theoretical and computational aspects. Zbl 07313349
Garrappa, Roberto
59
2015
Models of dielectric relaxation based on completely monotone functions. Zbl 1499.78010
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
51
2016
Explicit methods for fractional differential equations and their stability properties. Zbl 1169.65121
Galeone, Luciano; Garrappa, Roberto
48
2009
The Prabhakar or three parameter Mittag-Leffler function: theory and application. Zbl 1524.33083
Garra, Roberto; Garrappa, Roberto
46
2018
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
46
2020
On multistep methods for differential equations of fractional order. Zbl 1167.65399
Galeone, Luciano; Garrappa, Roberto
43
2006
Computing the matrix Mittag-Leffler function with applications to fractional calculus. Zbl 1406.65031
Garrappa, Roberto; Popolizio, Marina
36
2018
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085
Mainardi, Francesco; Garrappa, Roberto
35
2015
On some explicit Adams multistep methods for fractional differential equations. Zbl 1171.65098
Garrappa, Roberto
33
2009
Why fractional derivatives with nonsingular kernels should not be used. Zbl 1474.26020
Diethelm, Kai; Garrappa, Roberto; Giusti, Andrea; Stynes, Martin
33
2020
Solving the time-fractional Schrödinger equation by Krylov projection methods. Zbl 1349.65547
Garrappa, Roberto; Moret, Igor; Popolizio, Marina
32
2015
Evaluation of generalized Mittag-Leffler functions on the real line. Zbl 1272.33020
Garrappa, Roberto; Popolizio, Marina
32
2013
Generalized exponential time differencing methods for fractional order problems. Zbl 1228.65235
Garrappa, Roberto; Popolizio, Marina
31
2011
Fractional Adams-Moulton methods. Zbl 1163.65099
Galeone, Luciano; Garrappa, Roberto
31
2008
On the use of matrix functions for fractional partial differential equations. Zbl 1210.65162
Garrappa, Roberto; Popolizio, Marina
30
2011
On accurate product integration rules for linear fractional differential equations. Zbl 1206.65176
Garrappa, Roberto; Popolizio, Marina
28
2011
Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models. Zbl 1471.47032
Garrappa, Roberto
22
2016
Variable-order fractional calculus: a change of perspective. Zbl 1471.26002
Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco
21
2021
A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation. Zbl 1314.65130
Esmaeili, Shahrokh; Garrappa, Roberto
16
2015
Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching. Zbl 1345.37095
Danca, Marius-F.; Garrappa, Roberto; Tang, Wallace K. S.; Chen, Guanrong
16
2013
On the time-fractional Schrödinger equation: theoretical analysis and numerical solution by matrix Mittag-Leffler functions. Zbl 1448.65099
Garrappa, Roberto; Moret, Igor; Popolizio, Marina
15
2017
Nonstandard finite difference schemes for a fractional-order Brusselator system. Zbl 1380.65136
Ongun, Mevlüde Yakıt; Arslan, Damla; Garrappa, Roberto
14
2013
A family of Adams exponential integrators for fractional linear systems. Zbl 1350.65078
Garrappa, Roberto
12
2013
On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019
Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco
11
2017
Stability-preserving high-order methods for multiterm fractional differential equations. Zbl 1258.34011
Garrappa, Roberto
11
2012
Suppressing chaos in discontinuous systems of fractional order by active control. Zbl 1338.34112
Danca, Marius-F.; Garrappa, Roberto
10
2015
An analysis of convergence for two-stage waveform relaxation methods. Zbl 1059.65067
Garrappa, Roberto
9
2004
On Volterra functions and Ramanujan integrals. Zbl 1342.45001
Garrappa, Roberto; Mainardi, Francesco
8
2016
On some generalizations of the implicit Euler method for discontinuous fractional differential equations. Zbl 07312537
Garrappa, Roberto
8
2014
Exponential quadrature rules for linear fractional differential equations. Zbl 1314.65093
Garrappa, Roberto; Popolizio, Marina
7
2015
Some formulas for sums of binomial coefficients and gamma functions. Zbl 1162.11015
Garrappa, Roberto
6
2007
Fractional Prabhakar derivative and applications in anomalous dielectrics: a numerical approach. Zbl 1428.82075
Garrappa, Roberto; Maione, Guido
6
2017
On initial conditions for fractional delay differential equations. Zbl 1480.34103
Garrappa, Roberto; Kaslik, Eva
6
2020
Order conditions for Volterra Runge-Kutta methods. Zbl 1197.65225
Garrappa, Roberto
5
2010
Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations. Zbl 1464.65083
Garrappa, Roberto
5
2019
Stability of fractional-order systems with Prabhakar derivatives. Zbl 1517.34005
Garrappa, Roberto; Kaslik, Eva
5
2020
Effect of perturbation in the numerical solution of fractional differential equations. Zbl 1402.65067
Garrappa, Roberto; Messina, Eleonora; Vecchio, Antonia
5
2018
A computationally efficient strategy for time-fractional diffusion-reaction equations. Zbl 1524.65339
Garrappa, Roberto; Popolizio, Marina
4
2022
Some results on the complete monotonicity of Mittag-Leffler functions of le Roy type. Zbl 1478.33010
Górska, Katarzyna; Horzela, Andrzej; Garrappa, Roberto
4
2019
An analysis of solutions to fractional neutral differential equations with delay. Zbl 1468.34105
Tuan, Hoang The; Thai, Ha Duc; Garrappa, Roberto
3
2021
A comparison of some explicit methods for fractional differential equations. Zbl 1167.65471
Garrappa, Roberto
2
2008
Convergence analysis of time-point relaxation iterates for linear systems of differential equations. Zbl 0885.65085
Galeone, Luciano; Garrappa, Roberto
1
1997
On the fractional Laplacian of variable order. Zbl 1503.35253
Darve, Eric; D’Elia, Marta; Garrappa, Roberto; Giusti, Andrea; Rubio, Natalia L.
1
2022
A computationally efficient strategy for time-fractional diffusion-reaction equations. Zbl 1524.65339
Garrappa, Roberto; Popolizio, Marina
4
2022
On the fractional Laplacian of variable order. Zbl 1503.35253
Darve, Eric; D’Elia, Marta; Garrappa, Roberto; Giusti, Andrea; Rubio, Natalia L.
1
2022
Variable-order fractional calculus: a change of perspective. Zbl 1471.26002
Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco
21
2021
An analysis of solutions to fractional neutral differential equations with delay. Zbl 1468.34105
Tuan, Hoang The; Thai, Ha Duc; Garrappa, Roberto
3
2021
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
46
2020
Why fractional derivatives with nonsingular kernels should not be used. Zbl 1474.26020
Diethelm, Kai; Garrappa, Roberto; Giusti, Andrea; Stynes, Martin
33
2020
On initial conditions for fractional delay differential equations. Zbl 1480.34103
Garrappa, Roberto; Kaslik, Eva
6
2020
Stability of fractional-order systems with Prabhakar derivatives. Zbl 1517.34005
Garrappa, Roberto; Kaslik, Eva
5
2020
Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations. Zbl 1464.65083
Garrappa, Roberto
5
2019
Some results on the complete monotonicity of Mittag-Leffler functions of le Roy type. Zbl 1478.33010
Górska, Katarzyna; Horzela, Andrzej; Garrappa, Roberto
4
2019
Numerical solution of fractional differential equations: a survey and a software tutorial. Zbl 06916890
Garrappa, Roberto
97
2018
The Prabhakar or three parameter Mittag-Leffler function: theory and application. Zbl 1524.33083
Garra, Roberto; Garrappa, Roberto
46
2018
Computing the matrix Mittag-Leffler function with applications to fractional calculus. Zbl 1406.65031
Garrappa, Roberto; Popolizio, Marina
36
2018
Effect of perturbation in the numerical solution of fractional differential equations. Zbl 1402.65067
Garrappa, Roberto; Messina, Eleonora; Vecchio, Antonia
5
2018
On the time-fractional Schrödinger equation: theoretical analysis and numerical solution by matrix Mittag-Leffler functions. Zbl 1448.65099
Garrappa, Roberto; Moret, Igor; Popolizio, Marina
15
2017
On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019
Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco
11
2017
Fractional Prabhakar derivative and applications in anomalous dielectrics: a numerical approach. Zbl 1428.82075
Garrappa, Roberto; Maione, Guido
6
2017
Models of dielectric relaxation based on completely monotone functions. Zbl 1499.78010
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
51
2016
Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models. Zbl 1471.47032
Garrappa, Roberto
22
2016
On Volterra functions and Ramanujan integrals. Zbl 1342.45001
Garrappa, Roberto; Mainardi, Francesco
8
2016
Numerical evaluation of two and three parameter Mittag-Leffler functions. Zbl 1331.33043
Garrappa, Roberto
89
2015
Trapezoidal methods for fractional differential equations: theoretical and computational aspects. Zbl 07313349
Garrappa, Roberto
59
2015
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085
Mainardi, Francesco; Garrappa, Roberto
35
2015
Solving the time-fractional Schrödinger equation by Krylov projection methods. Zbl 1349.65547
Garrappa, Roberto; Moret, Igor; Popolizio, Marina
32
2015
A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation. Zbl 1314.65130
Esmaeili, Shahrokh; Garrappa, Roberto
16
2015
Suppressing chaos in discontinuous systems of fractional order by active control. Zbl 1338.34112
Danca, Marius-F.; Garrappa, Roberto
10
2015
Exponential quadrature rules for linear fractional differential equations. Zbl 1314.65093
Garrappa, Roberto; Popolizio, Marina
7
2015
On some generalizations of the implicit Euler method for discontinuous fractional differential equations. Zbl 07312537
Garrappa, Roberto
8
2014
Evaluation of generalized Mittag-Leffler functions on the real line. Zbl 1272.33020
Garrappa, Roberto; Popolizio, Marina
32
2013
Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching. Zbl 1345.37095
Danca, Marius-F.; Garrappa, Roberto; Tang, Wallace K. S.; Chen, Guanrong
16
2013
Nonstandard finite difference schemes for a fractional-order Brusselator system. Zbl 1380.65136
Ongun, Mevlüde Yakıt; Arslan, Damla; Garrappa, Roberto
14
2013
A family of Adams exponential integrators for fractional linear systems. Zbl 1350.65078
Garrappa, Roberto
12
2013
Stability-preserving high-order methods for multiterm fractional differential equations. Zbl 1258.34011
Garrappa, Roberto
11
2012
Generalized exponential time differencing methods for fractional order problems. Zbl 1228.65235
Garrappa, Roberto; Popolizio, Marina
31
2011
On the use of matrix functions for fractional partial differential equations. Zbl 1210.65162
Garrappa, Roberto; Popolizio, Marina
30
2011
On accurate product integration rules for linear fractional differential equations. Zbl 1206.65176
Garrappa, Roberto; Popolizio, Marina
28
2011
On linear stability of predictor-corrector algorithms for fractional differential equations. Zbl 1206.65197
Garrappa, Roberto
83
2010
Order conditions for Volterra Runge-Kutta methods. Zbl 1197.65225
Garrappa, Roberto
5
2010
Explicit methods for fractional differential equations and their stability properties. Zbl 1169.65121
Galeone, Luciano; Garrappa, Roberto
48
2009
On some explicit Adams multistep methods for fractional differential equations. Zbl 1171.65098
Garrappa, Roberto
33
2009
Fractional Adams-Moulton methods. Zbl 1163.65099
Galeone, Luciano; Garrappa, Roberto
31
2008
A comparison of some explicit methods for fractional differential equations. Zbl 1167.65471
Garrappa, Roberto
2
2008
Some formulas for sums of binomial coefficients and gamma functions. Zbl 1162.11015
Garrappa, Roberto
6
2007
On multistep methods for differential equations of fractional order. Zbl 1167.65399
Galeone, Luciano; Garrappa, Roberto
43
2006
An analysis of convergence for two-stage waveform relaxation methods. Zbl 1059.65067
Garrappa, Roberto
9
2004
Convergence analysis of time-point relaxation iterates for linear systems of differential equations. Zbl 0885.65085
Galeone, Luciano; Garrappa, Roberto
1
1997
all top 5

Cited by 1,174 Authors

36 Garrappa, Roberto
20 Băleanu, Dumitru I.
17 Zheng, Xiangcheng
16 Wang, Hong
13 Ghanbari, Behzad
12 Gómez-Aguilar, José Francisco
12 Górska, Katarzyna
12 Popolizio, Marina
11 Li, Changpin
10 Giusti, Andrea
10 Horzela, Andrzej
10 Javidi, Mohammad
10 Zeng, Fanhai
8 Fernandez, Arran
8 Khaliq, Abdul Q. M.
8 Mainardi, Francesco
7 Cardone, Angelamaria
7 Garra, Roberto
7 Polito, Federico
7 Saad, Khaled Mohammed
6 Ansari, Alireza
6 Čermák, Jan
6 Danca, Marius-Florin
6 Furati, Khaled M.
6 Kumar, Sunil
6 Pogány, Tibor K.
6 Sandev, Trifce
6 Tomovski, Živorad
6 Turner, Ian William
5 Bhrawy, Ali Hassan
5 Conte, Dajana
5 Djilali, Salih
5 Durastante, Fabio
5 Esmaeili, Shahrokh
5 Heris, Mahdi Saedshoar
5 Liu, Fawang
5 Moret, Igor
5 Paternoster, Beatrice
5 Pedas, Arvet
5 Sene, Ndolane
5 Srivastava, Hari Mohan
5 Sun, Hongguang
5 Tarasov, Vasily E.
5 Wang, Dongling
4 Abdeljawad, Thabet
4 Aminataei, Azim
4 Burrage, Kevin
4 Colombaro, Ivano
4 Diethelm, Kai
4 Ding, Hengfei
4 Eshaghi, Shiva
4 Hamdan, Nur ’Izzati
4 Huang, Ting-Zhu
4 Jannelli, Alessandra
4 Jia, Jinhong
4 Kiliçman, Adem
4 Li, Yu
4 Lopez, Luciano
4 Machado, José António Tenreiro
4 Nechvátal, Luděk
4 Novati, Paolo
4 Owolabi, Kolade Matthew
4 Pellegrino, Sabrina Francesca
4 Samei, Mohammad Esmael
4 Sarumi, Ibrahim O.
4 Tuan, Hoang The
4 Ur Rehman, Mujeeb
4 Zaky, Mahmoud A.
3 Aceto, Lidia
3 Agahi, Hamzeh
3 Antoine, Xavier
3 Bazhlekova, Emilia G.
3 Biala, Toheeb A.
3 Chechkin, Aleksei V.
3 Chen, Yangquan
3 Chu, Yuming
3 D’Ambrosio, Raffaele
3 Das, Amiya
3 Dattoli, Giuseppe
3 de Oliveira, Edmundo Capelas
3 Deng, Weihua
3 Derakhshan, Mohammadhossein
3 D’Ovidio, Mirko
3 Estrada, Ernesto
3 Fan, Zhencheng
3 Hendy, Ahmed S.
3 Hicdurmaz, Betul
3 Inc, Mustafa
3 Jiang, Xiaoyun
3 Karniadakis, George Em
3 Kisela, Tomáš
3 Kumar, Devendra
3 Kürt, Cemaliye
3 Lattanzi, Ambra
3 Liang, Xiao
3 Matignon, Denis
3 Mehrez, Khaled
3 Metzler, Ralf
3 Michelitsch, Thomas M.
3 Mustapha, Kassem
...and 1,074 more Authors
all top 5

Cited in 172 Serials

47 Fractional Calculus & Applied Analysis
45 Chaos, Solitons and Fractals
34 Journal of Computational and Applied Mathematics
34 Advances in Difference Equations
28 Communications in Nonlinear Science and Numerical Simulation
26 Applied Numerical Mathematics
25 Computational and Applied Mathematics
22 Computers & Mathematics with Applications
22 Applied Mathematics and Computation
22 Mathematics and Computers in Simulation
21 International Journal of Computer Mathematics
16 Mathematical Methods in the Applied Sciences
14 Journal of Scientific Computing
12 Physica A
12 Numerical Algorithms
12 Nonlinear Dynamics
10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
9 Journal of Computational Physics
9 Integral Transforms and Special Functions
9 Chaos
8 Applied Mathematical Modelling
8 International Journal of Nonlinear Sciences and Numerical Simulation
8 Mediterranean Journal of Mathematics
7 Numerical Methods for Partial Differential Equations
6 SIAM Journal on Numerical Analysis
6 Applied Mathematics Letters
6 SIAM Journal on Scientific Computing
6 Abstract and Applied Analysis
6 Journal of Physics A: Mathematical and Theoretical
6 Mathematics
6 Journal of Function Spaces
5 Fractals
5 Advances in Computational Mathematics
5 Journal of Applied Mathematics and Computing
5 S\(\vec{\text{e}}\)MA Journal
5 International Journal of Applied and Computational Mathematics
4 Journal of the Franklin Institute
4 BIT
4 Mathematical Problems in Engineering
4 Discrete and Continuous Dynamical Systems. Series S
4 Fractional Differential Calculus
3 Acta Mechanica
3 Bulletin of Mathematical Biology
3 Calcolo
3 International Journal of Mathematics and Mathematical Sciences
3 Numerical Functional Analysis and Optimization
3 Qualitative Theory of Dynamical Systems
3 Journal of Applied Mathematics
3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
3 Journal of Mathematics
3 Iranian Journal of Numerical Analysis and Optimization
3 Computational Methods for Differential Equations
3 Open Mathematics
3 International Journal of Systems Science. Principles and Applications of Systems and Integration
2 Computer Physics Communications
2 Physics Letters. A
2 Reports on Mathematical Physics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Journal of Differential Equations
2 Journal of Functional Analysis
2 Stochastic Analysis and Applications
2 SIAM Journal on Matrix Analysis and Applications
2 SIAM Journal on Applied Mathematics
2 Journal of the Egyptian Mathematical Society
2 Complexity
2 Engineering Analysis with Boundary Elements
2 Journal of Difference Equations and Applications
2 Differential Equations and Dynamical Systems
2 Analysis (München)
2 Mathematical Modelling and Analysis
2 Matematicheskoe Modelirovanie
2 Analysis and Applications (Singapore)
2 Inverse Problems in Science and Engineering
2 Mathematical Modelling of Natural Phenomena
2 Journal of Pseudo-Differential Operators and Applications
2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
2 Symmetry
2 Axioms
2 Journal of Applied Nonlinear Dynamics
2 Journal of Mathematical Modeling
2 Modern Stochastics. Theory and Applications
2 AIMS Mathematics
2 Advances in Continuous and Discrete Models
1 Analysis Mathematica
1 Computer Methods in Applied Mechanics and Engineering
1 Inverse Problems
1 Journal of Engineering Mathematics
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Journal of Statistical Physics
1 Mathematical Notes
1 Mathematics of Computation
1 Canadian Journal of Mathematics
1 Demonstratio Mathematica
1 Journal of Approximation Theory
1 Numerische Mathematik
1 Pacific Journal of Mathematics
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Revista de la Unión Matemática Argentina
1 Studies in Applied Mathematics
...and 72 more Serials
all top 5

Cited in 44 Fields

352 Numerical analysis (65-XX)
313 Ordinary differential equations (34-XX)
225 Real functions (26-XX)
215 Partial differential equations (35-XX)
98 Special functions (33-XX)
87 Biology and other natural sciences (92-XX)
48 Integral equations (45-XX)
44 Probability theory and stochastic processes (60-XX)
39 Systems theory; control (93-XX)
38 Dynamical systems and ergodic theory (37-XX)
32 Integral transforms, operational calculus (44-XX)
22 Operator theory (47-XX)
21 Mechanics of deformable solids (74-XX)
21 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
19 Fluid mechanics (76-XX)
18 Statistical mechanics, structure of matter (82-XX)
16 Approximations and expansions (41-XX)
15 Linear and multilinear algebra; matrix theory (15-XX)
12 Difference and functional equations (39-XX)
11 Optics, electromagnetic theory (78-XX)
9 Calculus of variations and optimal control; optimization (49-XX)
8 Information and communication theory, circuits (94-XX)
7 Functions of a complex variable (30-XX)
6 Statistics (62-XX)
6 Mechanics of particles and systems (70-XX)
6 Quantum theory (81-XX)
5 Measure and integration (28-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Classical thermodynamics, heat transfer (80-XX)
5 Operations research, mathematical programming (90-XX)
4 Combinatorics (05-XX)
4 Functional analysis (46-XX)
4 Geophysics (86-XX)
3 Potential theory (31-XX)
3 Computer science (68-XX)
2 Number theory (11-XX)
2 Topological groups, Lie groups (22-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Sequences, series, summability (40-XX)
1 Abstract harmonic analysis (43-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Mathematics education (97-XX)

Citations by Year