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Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial

Dipartimento di Matematica, Università Degli Studi di Bari, Via E. Orabona 4, 70126 Bari, Italy
Mathematics 2018, 6(2), 16; https://doi.org/10.3390/math6020016
Received: 8 December 2017 / Revised: 10 January 2018 / Accepted: 14 January 2018 / Published: 23 January 2018
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and efficient way is much more difficult than in the standard integer-order case; moreover, the majority of the computational tools do not provide built-in functions for this kind of problem. In this paper, we review two of the most effective families of numerical methods for fractional-order problems, and we discuss some of the major computational issues such as the efficient treatment of the persistent memory term and the solution of the nonlinear systems involved in implicit methods. We present therefore a set of MATLAB routines specifically devised for solving three families of fractional-order problems: fractional differential equations (FDEs) (also for the non-scalar case), multi-order systems (MOSs) of FDEs and multi-term FDEs (also for the non-scalar case); some examples are provided to illustrate the use of the routines. View Full-Text
Keywords: fractional differential equations (FDEs); numerical methods; multi-order systems (MOSs); multi-term equations; product integration (PI); fractional linear multi-step methods (FLMMs); MATLAB routines fractional differential equations (FDEs); numerical methods; multi-order systems (MOSs); multi-term equations; product integration (PI); fractional linear multi-step methods (FLMMs); MATLAB routines
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MDPI and ACS Style

Garrappa, R. Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial. Mathematics 2018, 6, 16. https://doi.org/10.3390/math6020016

AMA Style

Garrappa R. Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial. Mathematics. 2018; 6(2):16. https://doi.org/10.3390/math6020016

Chicago/Turabian Style

Garrappa, Roberto. 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial" Mathematics 6, no. 2: 16. https://doi.org/10.3390/math6020016

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