Numerical solution of multiterm fractional differential equations using the matrix Mittag-Leffler functions
type: Item
instance of: scholarly article
title: Numerical solution of multiterm fractional differential equations using the matrix Mittag-Leffler functions
author: Marina Popolizio
published in: Mathematics
publication date: 2018-08-13T00:00:00Z
review text: Summary: Multiterm fractional differential equations (MTFDEs) nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs) to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag-Leffler (ML) functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.
Mathematics Subject Classification ID: 65-XX
Mathematics Subject Classification ID: 34-XX
Mathematics Subject Classification ID: 60-XX
zbMATH DE Number: 6916882
zbMATH Keywords: fractional differential equations
zbMATH Keywords: multiterm differential equations
zbMATH Keywords: Mittag-Leffler function
zbMATH Keywords: matrix function
zbMATH Keywords: fractional calculus
describes a project that uses: ML
describes a project that uses: FracPECE
MaRDI profile type: Publication
full work available at URL: math6010007
OpenAlex ID: W2782855242
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DOI: 10.3390/MATH6010007
description: scientific article; zbMATH DE number 6916882