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Open AccessFeature PaperArticle

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

1
Fakultät Angewandte Natur- und Geisteswissenschaften, University of Applied Sciences Würzburg-Schweinfurt, Ignaz-Schön-Str. 11, 97421 Schweinfurt, Germany
2
GNS mbH Gesellschaft für Numerische Simulation mbH, Am Gaußberg 2, 38114 Braunschweig, Germany
3
Department of Mathematics, University of Bari, Via E. Orabona 4, 70126 Bari, Italy
4
INdAM Research Group GNCS, Piazzale Aldo Moro 5, 00185 Rome, Italy
5
Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 324; https://doi.org/10.3390/math8030324
Received: 26 January 2020 / Revised: 24 February 2020 / Accepted: 25 February 2020 / Published: 2 March 2020
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware of the specific difficulties. As a consequence, numerical methods are often applied in an incorrect way or unreliable methods are devised and proposed in the literature. In this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list some good practices that should be followed in order to obtain correct results. View Full-Text
Keywords: fractional differential equations; numerical methods; smoothness assumptions; persistent memory fractional differential equations; numerical methods; smoothness assumptions; persistent memory
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MDPI and ACS Style

Diethelm, K.; Garrappa, R.; Stynes, M. Good (and Not So Good) Practices in Computational Methods for Fractional Calculus. Mathematics 2020, 8, 324.

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