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Algorithms for the fractional calculus: a selection of numerical methods. (English) Zbl 1119.65352
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.
65L05Initial value problems for ODE (numerical methods)
26A33Fractional derivatives and integrals (real functions)
34A34Nonlinear ODE and systems, general
65D32Quadrature and cubature formulas (numerical methods)
65D25Numerical differentiation
65E05Numerical methods in complex analysis