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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.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
26A33 Fractional derivatives and integrals
34A34 Nonlinear ordinary differential equations and systems
65D32 Numerical quadrature and cubature formulas
65D25 Numerical differentiation
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
Software:
NAG; nag; QUADPACK
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