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1

Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions

Garrappa, Roberto

Journal:

SIAM Journal on Numerical Analysis

Year:

2015

Language:

english

File:

PDF, 285 KB

english, 2015

2

The Prabhakar or three parameter Mittag–Leffler function: theory and application

Garra, Roberto, Garrappa, Roberto

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2017

Language:

english

File:

PDF, 967 KB

english, 2017

3

Computing the Matrix Mittag-Leffler Function with Applications to Fractional Calculus

Garrappa, Roberto, Popolizio, Marina

Journal:

Journal of Scientific Computing

Year:

2018

Language:

english

File:

PDF, 956 KB

english, 2018

4

On the use of matrix functions for fractional partial differential equations

Roberto Garrappa, Marina Popolizio

Journal:

Mathematics and Computers in Simulation

Year:

2011

Language:

english

File:

PDF, 282 KB

english, 2011

5

Pseudo-recursive Trapezoidal Rule for the Numerical Solution of Linear Fractional Differential Equations * *The work of A. Pisano, D. Nessi and R. Garrappa has been supported by the Italian Ministry of University and Research (MIUR) under project “Non integer order systems in modelling and control”, Grant no. 2009F4NZJP. A. Pisano also acknowledges funding from the European Union Seventh Framework Programme (FP7/2007-2013) Network of excellence “HYCON2-Highly-complex and networked control systems” under grant agreement n. 257462. M. R. Rapaić gratefully acknowledges the support of Serbian Ministry of Education and Science, grant no. 32018.

Pisano, Alessandro, Garrappa, Roberto, Nessi, Davide, Rapaić, Milan R.

Journal:

IFAC Proceedings Volumes

Year:

2013

Language:

english

File:

PDF, 318 KB

english, 2013

6

Generalized exponential time differencing methods for fractional order problems

Roberto Garrappa, Marina Popolizio

Journal:

Computers & Mathematics with Applications

Year:

2011

Language:

english

File:

PDF, 532 KB

english, 2011

7

Fractional Adams–Moulton methods

Luciano Galeone, Roberto Garrappa

Journal:

Mathematics and Computers in Simulation

Year:

2008

Language:

english

File:

PDF, 172 KB

english, 2008

8

On linear stability of predictor–corrector algorithms for fractional differential equations

Garrappa, Roberto

Journal:

International Journal of Computer Mathematics

Year:

2010

Language:

english

File:

PDF, 267 KB

english, 2010

9

Trapezoidal methods for fractional differential equations: Theoretical and computational aspects

Garrappa, Roberto

Journal:

Mathematics and Computers in Simulation

Year:

2015

Language:

english

File:

PDF, 1.20 MB

english, 2015

10

On Volterra functions and Ramanujan integrals

Garrappa, Roberto, Mainardi, Francesco

Journal:

Analysis (Oldenbourg Wissenschaftsverlag)

Year:

2015

Language:

english

File:

PDF, 1.12 MB

english, 2015

11

On the time-fractional Schrödinger equation: Theoretical analysis and numerical solution by matrix Mittag-Leffler functions

Garrappa, Roberto, Moret, Igor, Popolizio, Marina

Journal:

Computers & Mathematics with Applications

Year:

2016

Language:

english

File:

PDF, 650 KB

english, 2016

12

Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial

Garrappa, Roberto

Journal:

Year:

2018

Language:

english

File:

PDF, 647 KB

english, 2018

13

Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type

Górska, Katarzyna, Horzela, Andrzej, Garrappa, Roberto

Journal:

Fractional Calculus and Applied Analysis

Year:

2019

File:

PDF, 429 KB

2019

14

A practical guide to Prabhakar fractional calculus

Giusti, Andrea, Colombaro, Ivano, Garra, Roberto, Garrappa, Roberto, Polito, Federico, Popolizio, Marina, Mainardi, Francesco

Journal:

Fractional Calculus and Applied Analysis

Year:

2020

File:

PDF, 591 KB

2020

15

Good (and Not So Good) Practices in Computational Methods for Fractional Calculus

Diethelm, Kai, Garrappa, Roberto, Stynes, Martin

Journal:

Year:

2020

File:

PDF, 358 KB

2020

16

Order conditions for Volterra Runge–Kutta methods

Roberto Garrappa

Journal:

Applied Numerical Mathematics

Year:

2010

Language:

english

File:

PDF, 256 KB

english, 2010

17

The use of geometric meshes in product integration Simpson's rules

Roberto Garrappa

Journal:

Journal of Computational and Applied Mathematics

Year:

2007

Language:

english

File:

PDF, 190 KB

english, 2007

18

Explicit methods for fractional differential equations and their stability properties

Luciano Galeone, Roberto Garrappa

Journal:

Journal of Computational and Applied Mathematics

Year:

2009

Language:

english

File:

PDF, 1.01 MB

english, 2009

19

Evaluation of generalized Mittag–Leffler functions on the real line

Roberto Garrappa, Marina Popolizio

Journal:

Advances in Computational Mathematics

Year:

2013

Language:

english

File:

PDF, 421 KB

english, 2013

20

Exponential Quadrature Rules for Linear Fractional Differential Equations

Garrappa, Roberto, Popolizio, Marina

Journal:

Mediterranean Journal of Mathematics

Year:

2015

Language:

english

File:

PDF, 520 KB

english, 2015

21

On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics

Mainardi, Francesco, Garrappa, Roberto

Journal:

Journal of Computational Physics

Year:

2015

Language:

english

File:

PDF, 807 KB

english, 2015

22

Suppressing chaos in discontinuous systems of fractional order by active control

Danca, Marius-F., Garrappa, Roberto

Journal:

Applied Mathematics and Computation

Year:

2015

Language:

english

File:

PDF, 2.23 MB

english, 2015

23

A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation

Esmaeili, Shahrokh, Garrappa, Roberto

Journal:

International Journal of Computer Mathematics

Year:

2015

Language:

english

File:

PDF, 382 KB

english, 2015

24

STABILITY-PRESERVING HIGH-ORDER METHODS FOR MULTITERM FRACTIONAL DIFFERENTIAL EQUATIONS

GARRAPPA, ROBERTO

Journal:

International Journal of Bifurcation and Chaos

Year:

2012

Language:

english

File:

PDF, 256 KB

english, 2012

25

[IEEE 2014 International Conference on Fractional Differentiation and its Applications (ICFDA) - Catania (2014.6.23-2014.6.25)] ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014 - Time-domain simulation for fractional relaxation of Havriliak-Negami type

Garrappa, Roberto, Maione, Guido, Popolizio, Marina

Year:

2014

Language:

english

File:

PDF, 314 KB

english, 2014

26

Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models

Garrappa, Roberto

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2016

Language:

english

File:

PDF, 966 KB

english, 2016

27

Models of dielectric relaxation based on completely monotone functions

Garrappa, Roberto, Mainardi, Francesco, Guido, Maione

Journal:

Fractional Calculus and Applied Analysis

Year:

2016

Language:

english

File:

PDF, 1021 KB

english, 2016

28

Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations

Garrappa, Roberto

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2019

Language:

english

File:

PDF, 732 KB

english, 2019

29

Corrigendum to “Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations” [Commun. Nonlinear Sci. Numer. Simulat. 70 (2019) 302–306]

Garrappa, Roberto

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2019

Language:

english

File:

PDF, 260 KB

english, 2019

30

Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial

Garrappa, Roberto, Kaslik, Eva, Popolizio, Marina

Journal:

Year:

2019

Language:

english

File:

PDF, 425 KB

english, 2019

31

An analysis of convergence for two-stage waveform relaxation methods

Roberto Garrappa

Journal:

Journal of Computational and Applied Mathematics

Year:

2004

Language:

english

File:

PDF, 271 KB

english, 2004

32

On some explicit Adams multistep methods for fractional differential equations

Roberto Garrappa

Journal:

Journal of Computational and Applied Mathematics

Year:

2009

Language:

english

File:

PDF, 781 KB

english, 2009

33

On Multistep Methods for Differential Equations of Fractional Order

Luciano Galeone, Roberto Garrappa

Journal:

Mediterranean Journal of Mathematics

Year:

2006

Language:

english

File:

PDF, 318 KB

english, 2006

34

On accurate product integration rules for linear fractional differential equations

Roberto Garrappa, Marina Popolizio

Journal:

Journal of Computational and Applied Mathematics

Year:

2011

Language:

english

File:

PDF, 352 KB

english, 2011

35

Convergence analysis of time-point relaxation iterates for linear systems of differential equations

Luciano Galeone, Roberto Garrappa

Journal:

Journal of Computational and Applied Mathematics

Year:

1997

Language:

english

File:

PDF, 755 KB

english, 1997

36

A family of Adams exponential integrators for fractional linear systems

Garrappa, Roberto

Journal:

Computers & Mathematics with Applications

Year:

2013

Language:

english

File:

PDF, 368 KB

english, 2013

37

On some generalizations of the implicit Euler method for discontinuous fractional differential equations

Garrappa, Roberto

Journal:

Mathematics and Computers in Simulation

Year:

2014

Language:

english

File:

PDF, 474 KB

english, 2014

38

Nonstandard finite difference schemes for a fractional-order Brusselator system

Ongun, Mevlüde, Arslan, Damla, Garrappa, Roberto

Journal:

Advances in Difference Equations

Year:

2013

Language:

english

File:

PDF, 255 KB

english, 2013

39

Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching

Danca, Marius-F., Garrappa, Roberto, Tang, Wallace K.S., Chen, Guanrong

Journal:

Computers & Mathematics with Applications

Year:

2013

Language:

english

File:

PDF, 2.59 MB

english, 2013

40

Solving the time-fractional Schrödinger equation by Krylov projection methods

Garrappa, Roberto, Moret, Igor, Popolizio, Marina

Journal:

Journal of Computational Physics

Year:

2015

Language:

english

File:

PDF, 1.22 MB

english, 2015

41

AIP Conference Proceedings [American Institute of Physics NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008 - Psalidi, Kos (Greece) (16–20 September 2008)] - A Comparison of Some Explicit Methods for Fractional Differential Equations

Garrappa, Roberto

Year:

2008

Language:

english

File:

PDF, 345 KB

english, 2008

42

[IEEE 2014 International Conference on Fractional Differentiation and its Applications (ICFDA) - Catania (2014.6.23-2014.6.25)] ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014 - Fast evaluation of the Mittag-Leffler function on the imaginary axis

Popolizio, Marina, Garrappa, Roberto

Year:

2014

Language:

english

File:

PDF, 215 KB

english, 2014

43

[IEEE 2015 54th IEEE Conference on Decision and Control (CDC) - Osaka, Japan (2015.12.15-2015.12.18)] 2015 54th IEEE Conference on Decision and Control (CDC) - Modeling and numerical analysis of fractional-order dynamics in electro-injectors pipes

Garrappa, Roberto, Lino, Paolo, Maione, Guido, Saponaro, Fabrizio

Year:

2015

Language:

english

File:

PDF, 300 KB

english, 2015

44

SDS2014 Guest Editorial

Buono, Nicoletta Del, Garrappa, Roberto, Spaletta, Giulia

Journal:

Mathematics and Computers in Simulation

Year:

2016

Language:

english

File:

PDF, 115 KB

english, 2016

45

Model Optimization and Flow Rate Prediction in Electro-injectors of Diesel Injection Systems

Garrappa, Roberto, Lino, Paolo, Maione, Guido, Saponaro, Fabrizio

Journal:

IFAC-PapersOnLine

Year:

2016

Language:

english

File:

PDF, 460 KB

english, 2016

46

On a generalized three-parameter wright function of Le Roy type

Garrappa, Roberto, Rogosin, Sergei, Mainardi, Francesco

Journal:

Fractional Calculus and Applied Analysis

Language:

english

File:

PDF, 428 KB

english

47

Structural dynamical systems: Computational aspects

Garrappa, Roberto, Elia, Cinzia, Gerardo-Giorda, Luca, Pugliese, Alessandro, Vacca, Giuseppe

Journal:

Applied Numerical Mathematics

Year:

2020

File:

PDF, 127 KB

2020

48

On initial conditions for fractional delay differential equations

Garrappa, Roberto, Kaslik, Eva

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2020

File:

PDF, 1017 KB

2020

49

Stability of fractional-order systems with Prabhakar derivatives

Garrappa, Roberto, Kaslik, Eva

Journal:

Nonlinear Dynamics

Year:

2020

File:

PDF, 1.02 MB

2020

50

On the Kuzmin model in fractional Newtonian gravity

Giusti, Andrea, Garrappa, Roberto, Vachon, GeneviÃ¨ve

Journal:

The European Physical Journal Plus

Year:

2020

File:

PDF, 454 KB

2020