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Zbl 1119.65352
Diethelm, K.; Ford, N.J.; Freed, A.D.; Luchko, Yu.
Algorithms for the fractional calculus: a selection of numerical methods. (English)
[J] Comput. Methods Appl. Mech. Eng. 194, No. 6-8, 743-773 (2005). ISSN 0045-7825

Summary: 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.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
26A33 Fractional derivatives and integrals (real functions)
34A34 Nonlinear ODE and systems, general
65D32 Quadrature formulas (numerical methods)
65D25 Numerical differentiation
65E05 Numerical methods in complex analysis

Keywords: Riemann-Liouville integrals; Caputo derivatives; Caputo differential equations; Mittag-Leffler function; numerical algorithms

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Zentralblatt MATH Berlin [Germany]