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Papers and other publications of Roberto Garrappa - University of Bari - Italy


Roberto Garrappa: Publications

 

 

 

Papers in peer reviewed journals

 

R.Garrappa, M.Popolizio, 
A computationally efficient strategy for time-fractional diffusion-reaction equations
Computers & Mathematics with Applications, 2021, in press 
doi: 10.1016/j.camwa.2021.05.027
[Accepted version]

E.Darve, M.D’Elia, R.Garrappa, A.Giusti, N.L.Rubio
On the fractional Laplacian of variable order
Fractional Calculus and Applied Analysis, 2022, 25, 15-28
doi: 10.1007/s13540-021-00003-1
[Open Access]

R.Garrappa, A.Giusti, F.Mainardi
Variable-order fractional calculus: a change of perspective
Communications in Nonlinear Science and Numerical Simulation, 2021, 102, 105904
doi: https://doi.org/10.1016/j.cnsns.2021.105904
[Accepted version] [Video presentation]

P.Lino, G.Maione, R.Garrappa, S.Holm,
An approach to optimal integer and fractional-order modeling of electro-injectors in compression-ignition engines
Control Engineering Practice, 2021, 115, 104890
doi: 10.1016/j.conengprac.2021.104890

O.Brandibur, R.Garrappa, E.Kaslik
Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives
Mathematics, 2021, 9(8), 914
doi: 10.3390/math9080914
[Open Access] [Paper]

H.T. Tuan, H.D. Thai, R.Garrappa
An analysis of solutions to fractional neutral differential equations with delay
Communications in Nonlinear Science and Numerical Simulation, 2021, 100, 105854
doi: https://doi.org/10.1016/j.cnsns.2021.105854
[Preprint

S.Luo, F.L. Lewis, Y.Song, R.Garrappa
Dynamical analysis and accelerated optimal stabilization of the fractional-order self-sustained electromechanical seismograph system with fuzzy wavelet neural network
Nonlinear Dynamics, 2021, 104, 1389-1404
doi: https://doi.org/10.1007/s11071-021-06330-5
[Read on SharedIt]  

S.Luo, Y.Song, F.L.Lewis, R.Garrappa
Neuroadaptive Optimal Fixed-Time Synchronization and Its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems
IEEE Transactions on Cybernetics, 2021
doi: 10.1109/TCYB.2021.3121069

A.Giusti, R.Garrappa, G.Vachon
On the Kuzmin model in fractional Newtonian gravity
Eur. Phys. J. Plus, 2020, 135(10), 798
doi: 10.1140/epjp/s13360-020-00831-9
[Read on SharedIt] [Preprint

R.Garrappa, E.Kaslik
Stability of fractional-order systems with Prabhakar derivatives
Nonlinear Dynamics, 2020, 102 567-578
doi: 10.1007/s11071-020-05897-9
[Read on SharedIt] [Preprint

K.Diethelm, R.Garrappa, A.Giusti, M.Stynes
Why fractional derivatives with nonsingular kernels should not be used
Fractional Calculus and Applied Analysis, 2020, 23(3), 610-634
doi: 10.1515/fca-2020-0032
[Preprint]

R.Garrappa, E.Kaslik
On initial conditions for fractional delay differential equations
Communications in Nonlinear Science and Numerical Simulation, 2020, 90, 105359
doi: 10.1016/j.cnsns.2020.105359
[Preprint

K.Diethelm, R.Garrappa, M.Stynes
Good (and not so good) practices in computational methods for fractional calculus
Mathematics, 2020, 8(3), 324
doi: 10.3390/math8030324
[Open Access]

A. Giusti, I. Colombaro, R. Garra, R. Garrappa, F. Polito, M. Popolizio, F. Mainardi
A practical guide to Prabhakar fractional calculus
Fractional Calculus and Applied Analyisis, 2020, 23(1), 9-54
doi: 10.1515/fca-2020-0002
[Preprint] [Open Access]

K.Gorska, A.Horzela, R.Garrappa
Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
Fractional Calculus and Applied Analyisis, 2019, 22(5), 1284-1306
doi: 10.1515/fca-2019-0068
[Preprint] [Paper]

R.Garrappa, E.Kaslik, M.Popolizio, 
Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial
Mathematics 2019, 7(5), 407
doi: 10.3390/math7050407
[Free Access

Garrappa, R.
Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations
Communications in Nonlinear Science and Numerical Simulation, 2019, 70, 302-306
doi: 10.1016/j.cnsns.2018.11.004 - See also the corrigendum
[Preprint]

Garrappa, R. & Popolizio, M.
Computing the matrix Mittag-Leffler function with applications to fractional calculus
Journal of Scientific Computing, 2018, 17(1), 129-153
doi: https://doi.org/10.1007/s10915-018-0699-5
[Read on SharedIt] [Preprint]

Garrappa, R. & Messina, E. & Vecchio, A.
Effect of perturbation in the numerical solution of fractional differential equations
Discrete and Continuous Dynamical Systems - Series B2018, 23(7), 2679-2694
doi: https://doi.org/
10.3934/dcdsb.2017188
[Paper]

Garrappa, R.
Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial
Mathematics 2018, 6(2), 16 
doi: https://doi.org/10.3390/math6020016
[Free access] [Matlab codes related to this paper]

Garra, R. & Garrappa, R.
The Prabhakar or three parameter Mittag--Leffler function: theory and application
Communications in Nonlinear Sciences and Numerical Simulation, 2018, 56, 314-329, 
doi: http://dx.doi.org/10.1016/j.cnsns.2017.08.018 
[Preprint

Garrappa, R & Mainardi, F. & Rogosin, S.
On a generalized Three-parameter Wright function of Le Roy type
Fractional Calculus and Applied Analyisis, 2017, 20(5), 1196-1215
doi: https://doi.org/10.1515/fca-2017-0063
[Free access]

Garrappa, R. & Moret, I. & Popolizio, M.
On the time-fractional Schrödinger equation: theoretical analysis and numerical solution by matrix Mittag-Leffler functions
Computers & Mathematics with Applications, 2017, 74(5), 977-992 
doi: http://dx.doi.org/10.1016/j.camwa.2016.11.028
[Preprint] [Paper]

Garrappa, R. & Mainardi, F. & Maione, G.
Models of dielectric relaxation based on completely monotone functions
Fractional Calculus & Applied Analysis, 2016, 19(5), 1105-1160
doi: http://dx.doi.org/10.1515/fca-2016-0060
[Paper] [BibTex]

Garrappa, R.
Grunwald-Letnikov operators for fractional relaxation in Havriliak-Negami models
Communications in Nonlinear Sciences and Numerical Simulation2016, 38, 178-191
doi: http://dx.doi.org/10.1016/j.cnsns.2016.02.015
[Preprint]

Garrappa, R. & Mainardi, F.
On Volterra functions and Ramanujan integrals
Analysis2016, 36(2), 89-105 
doi: http://dx.doi.org/10.1515/anly-2015-5009 
[Preprint]

Garrappa R. & Lino P & Maione G. & Saponaro F.
Model Optimization and Flow Rate Prediction in Electro-injectors of Diesel Injection Systems
IFAC PapersOnLine, 2016, 49(11), 484-489
doi: 10.1016/j.ifacol.2016.08.071
[Paper]

Garrappa, R.
Numerical Evaluation of two and three parameter Mittag-Leffler functions
SIAM Journal of Numerical Analysis, 2015, 53(3), 1350-1369
doi: http://dx.doi.org/10.1137/140971191
[Paper] - Matlab ml.m code published on Matlab Central

Garrappa, R. & Moret, I. & Popolizio, M.
Solving the time-fractional Schrödinger equation by Krylov projections methods
Journal of Computational Physics, 2015, 293, 115-134
doi: http://dx.doi.org/10.1016/j.jcp.2014.09.023
[Accepted Version

Mainardi, F. & Garrappa, R.
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
Journal of Computational Physics, 2015, 293, 70-80
doi: http://dx.doi.org/10.1016/j.jcp.2014.08.006 
[Accepted version]

Garrappa R.
Trapezoidal methods for fractional differential equations: theoretical and computational aspects
Mathematics and Computers in Simulation, 2015, 110, 96-112
doi: http://dx.doi.org/10.1016/j.matcom.2013.09.012
[Post-print] [ArXiv]

Danca, M.F. & Garrappa, R.
Suppressing chaos in discontinuous systems of fractional order by active control
Applied Mathematics and Computation, 2015, 257, 89-102
doi: http://dx.doi.org/10.1016/j.amc.2014.10.133
[
Preprint]

Esmaeili, S. & Garrappa, R.
A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation
International Journal of Computer Mathematics, 2015, 92(5) 980-994
doi: http://dx.doi.org/10.1080/00207160.2014.915962

Garrappa, R. & Popolizio, M.
Exponential quadrature rules for linear fractional differential equations
Mediterranean Journal of Mathematics, 201512(1)​ 219-244
doi: http://dx.doi.org/10.1007/s00009-014-0396-z
[Preprint] [View on SharedIt]

Garrappa, R.
On some generalizations of the implicit Euler method for discontinuous fractional differential equations
Mathematics and Computers in Simulation, 2014, 95, 213-228,
doi: http://dx.doi.org/10.1016/j.matcom.2012.04.009
[Preprint] [Paper]

Garrappa R.
Exponential integrators for time-fractional partial differential equations
Eur. Phys. J. Special Topics, 2013, 222, 1913–1925
doi: http://dx.doi.org/10.1140/epjst/e2013-01973-1
[Preprint] [Paper] [View on SharedIt]

Ongun M.Y. & Arslan D. & Garrappa R.
Nonstandard finite difference schemes for fractional order Brusselator system
Advances in Difference Equations 2013, 2013:102
doi: http://dx.doi.org/10.1186/1687-1847-2013-102
[Paper]

Danca, M.F. & Garrappa, R. & Tang, W.K.S. & Chen, G.
Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching
Computers & Mathematics with Applications, 2013, 66(5), 702-716,
doi: http://dx.doi.org/10.1016/j.camwa.2013.01.028
[Paper in open Archive]

Garrappa, R.
A family of Adams exponential integrators for fractional linear systems
Computers and Mathematics with Applications, 2013, 66(5), 717-727,
doi: http://dx.doi.org10.1016/j.camwa.2013.01.022
[Preprint] [Paper in open Archive]

Garrappa, R. & Popolizio M.
Evaluation of generalized Mittag–Leffler functions on the real line
Advances in Computational Mathematics, 2013, 39(1), 205-225,
doi: http://dx.doi.org/10.1007/s10444-012-9274-z
[Preprint] [Paper] [View on SharedIt]

Garrappa, R.
Stability-preserving high-order methods for multiterm fractional differential equations
International Journal of Bifurcation and Chaos, 2012, 22(4),
doi: http://dx.doi.org/10.1142/S0218127412500733

Garrappa, R. & Popolizio, M.
Generalized exponential time differencing methods for fractional order problems
Computers and Mathematics with Applications, 2011, 62(3), 876-890
doi: http://dx.doi.org/10.1016/j.camwa.2011.04.054
[Paper in open Archive

Garrappa, R. & Popolizio, M.
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation, 2011, 81(5), 1045-1056,
doi: http://dx.doi.org/10.1016/j.matcom.2010.10.009

Garrappa, R. & Popolizio, M.
On accurate product integration rules for linear fractional differential equations
Journal of Computational and Applied Mathematics, 2011, 235(5), 1085-1097
doi: http://dx.doi.org/10.1016/j.cam.2010.07.008

Garrappa, R.
On linear stability of predictor-corrector algorithms for fractional differential equations
International Journal of Computer Mathematics, 2010, 87(10), 2281-2290
doi: http://dx.doi.org/10.1080/00207160802624331

Garrappa, R.
Order conditions for Volterra Runge–Kutta methods
Applied Numerical Mathematics, 2010, 60(5), 561 - 573
doi: http://dx.doi.org/10.1016/j.apnum.2010.02.004
[Paper]

Garrappa, R.
On some explicit Adams multistep methods for fractional differential equations
Journal of Computational and Applied Mathematics, 2009, 229, 392 - 399
doi: http://dx.doi.org/10.1016/j.cam.2008.04.004
[Elsevier Open Archive]

Galeone, L. & Garrappa, R.
Explicit methods for fractional differential equations and their stability properties
Journal of Computational and Applied Mathematics, 2009, 228, 548 - 560
doi: http://dx.doi.org/10.1016/j.cam.2008.03.025
[Elsevier Open Archive]

Galeone, L. & Garrappa, R.
Fractional Adams-Moulton methods
Mathematics and Computers in Simulation, 2008, 79, 1358 - 1367
doi: http://dx.doi.org/10.1016/j.matcom.2008.03.008
[Paper]

Garrappa, R.
Some formulas for sums of binomial coefficients and gamma functions
Int. Math. Forum, 2007, 2, 725-733
[paper]

Garrappa, R.
The use of geometric meshes in product integration Simpson's rules
J. Comput. Appl. Math., 2007, 210, 200-209
[Elsevier Open Archive]

Galeone, L. & Garrappa, R.
On multistep methods for differential equations of fractional order
Mediterr. J. Math., 2006, 3(3), 565-580
doi: http://dx.doi.org/10.1007/s00009-006-0097-3 
[Paper] [View on SharedIt]

Garrappa, R.
An analysis of convergence for two-stage waveform relaxation methods
J. Comput. Appl. Math., 2004, 169, 377-392
[Elsevier Open Archive]

Galeone, L. & Garrappa, R.
Convergence analysis of time-point relaxation iterates for linear systems of differential equations
J. Comput. Appl. Math., 1997, 80, 183-195
[Paper]

 

Papers in peer reviewed proceedings

 

Garrappa R. & Lino P & Maione G. & Saponaro F.
Modeling and numerical analysis of fractional-order dynamics in electro-injectors pipes
Proceedings of the 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, December 15-18, 2015, 5984-5989
​doi: http://dx.doi.org/10.1109/CDC.2015.7403160​

Garrappa R.
On finite difference approximations of Havriliak-Negami operators 
In Non-linear systems, Nanotechnology, Recent Advances in Electrical Engineering Series, vol 55, p. 97-102, ISBN: 978-1-61804-345-0, ISSN: 1790-5117. Proceedings of the 14th International Conference on Non-Linear Analysis, NonLinear Systems and Chaos (NOLASC '15), Roma, Italy, November 7-9 2015.
[Paper

Garrappa R.
A Grunwald–Letnikov scheme for fractional operators of Havriliak–Negami type
In Mathematics and Computers in Science and Engineering Series, vol. 34, p. 70-76, ISBN: 978-960-474-398-8, ISSN: 2227-4588. Proceedings of the 8th International Conference on Applied Mathematics, Simulation, Modelling (ASM '14), Firenze, Italy, November 22-23 2014.
[Paper]

Garrappa R. & Maione G. & Popolizio M.
Time-domain simulation for factional relaxation of Havriliak-Negami type
Proceedings of the 2014 International Conference on Fractional Differentiation and Its Applications (ICFDA), Catania, Italy, June 23-25, 2014
doi: http://dx.doi.org/10.1109/ICFDA.2014.6967399

Garrappa R. & Popolizio M.
Fast evaluation of the Mittag-Leffler function on the imaginary axis
Proceedings of the 2014 International Conference on Fractional Differentiation and Its Applications (ICFDA), Catania, Italy, June 23-25, 2014
doi: http://dx.doi.org/10.1109/ICFDA.2014.6967420

Garrappa R. & Maione G.
Model Order Reduction on Krylov Subspaces for Fractional Linear Systems
Proceedings of the 6th Workshop on Fractional Differentiation and Its Applications, Part of 2013 IFAC Joint Conference SSSC, FDA, TDS, Grenoble, France, February 4-6, 2013
doi: http://dx.doi.org/10.3182/20130204-3-FR-4032.00138

Pisano A. & Garrappa R. & Nessi D. & Rapaic M.
Pseudo-Recursive Trapezoidal Rule for the Numerical Solution of Linear Fractional Differential Equations
Proceedings of the 6th Workshop on Fractional Differentiation and Its Applications, Part of 2013 IFAC Joint Conference SSSC, FDA, TDS, Grenoble, France, February 4-6, 2013
doi: http://dx.doi.org/10.3182/20130204-3-FR-4032.00150

Garrappa, R.
A family of Adams exponential integrators for fractional linear systems,
Proceedings of the 5th Workshop on Fractional Differentiation and Its Applications, Nanjing, China, May 14-17, 2012

Garrappa, R.
A comparison of some explicit methods for fractional differential equations 
AIP, 2008, 1048, 217-220

 

Chapter books

 

Garrappa R. & Popolizio M. 
Fast methods for the computation of the Mittag-Leffler function. In "Handbook of Fractional Calculus with Applications. Volume 3: Numerical Methods" (editor: George Em Karniadakis). De Gruyter (Berlin, Boston), 2019, pp. 329–346, ISBN: 978-3-11-057168-4 
doi: https://doi.org/10.1515/9783110571684-013
 

Garrappa, R. & Maione, G.
Fractional Prabhakar derivative and applications in anomalous dielectrics: a numerical approach. Chapter book in "Theory and Applications of Non-Integer Order Systems" (editors: Babiar, A., Czornik, A., Klamka, J., Niezabitowski, M.), Springer  2017, 429-439 ISBN: 978-3-319-45474-0, doi: http://dx.doi.org/10.1007/978-3-319-45474-0_38 
[Preprint]

Garrappa, R. & Popolizio, M.
Exponential Integrators for Fractional Differential Equations. Chapter book in "Fractional Calculus: Theory" (editors: Roy Abi Zeid Daou and Xavier Moreau), Nova Science Publishing (US) 2015. ISBN: 978-1-63463-027-6

 

Miscellanea

 

Beghin L, Mainardi F., Garrappa  (Editors)
Nonlocal and Fractional Operators
SEMA SIMAI Springer Book Series, 2021, vol. 26 
ISBN: 978-3-030-69238-4
doi: https://doi.org/10.1007/978-3-030-69236-0 

 

 

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