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

Kai Diethelm, Roberto Garrappa and Martin Stynes
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Kai Diethelm: Fakultät Angewandte Natur- und Geisteswissenschaften, University of Applied Sciences Würzburg-Schweinfurt, Ignaz-Schön-Str. 11, 97421 Schweinfurt, Germany
Roberto Garrappa: Department of Mathematics, University of Bari, Via E. Orabona 4, 70126 Bari, Italy
Martin Stynes: Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China

Mathematics, 2020, vol. 8, issue 3, 1-21

Abstract: 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.

Keywords: fractional differential equations; numerical methods; smoothness assumptions; persistent memory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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