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Publications of Roberto Garrappa - University of Bari - Italy


Roberto Garrappa: Publications

 

 

 

Papers in peer reviewed journals

 

 

Garrappa, R. & Kaslik, E. & Popolizio, M.
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]

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] [Free version until November 29, 2017]

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
[Preprint] [BibTex]

Garrappa, R.
On 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
[Preprint

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 
[Preprint]

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
[Preprint

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
doi: http://dx.doi.org/10.1007/s00009-006-0097-3 
Mediterr. J. Math., 2006, 3(3), 565-580
[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

 

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Pubblicato il: Jan 12, 2013  Ultima modifica: May 08, 2019
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