Algorithms for the fractional calculus: A selection of numerical methods

(with N. J. Ford, A. D. Freed and Y. Luchko)


Comput. Methods Appl. Mech. Eng. 194 (2005), 743-773.


2000 Mathematics Subject Classification: 65D25, 65D30, 65L05, 65R20.

Key words: Riemann-Liouville integrals, Caputo derivatives, Caputo differential equations, Mittag-Leffler function.


Abstract

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

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