An Algorithm for the Numerical Solution of Differential Equations
of Fractional Order
Elec. Transact. Numer. Anal. 5 (1997), 1-6.
[MR 98k:65037; Zbl. Math. 890.65071]
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text (PDF, 65 KBytes)
1991 Mathematics Subject Classification: 26A33, 65L70, 65L05.
Key words: Fractional derivative,
Riemann-Liouville derivative, differential equation,
numerical solution, quadrature formula, implicit method.
Abstract
Differential equations involving derivatives of non-integer order have
shown to be adequate models for various physical phenomena in areas like
damping laws, diffusion processes, etc. A small number of algorithms for the
numerical solution of these equations has been suggested, but mainly without
any error estimates. In this paper, we propose an implicit algorithm for the
approximate solution of an important class of these equations. The
algorithm is based on a quadrature formula approach. Error
estimates and numerical examples are given.
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