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On a numerical scheme for solving differential equations of fractional order. (English) Zbl 1258.65103
From the summary: In this work, on the basis of a modified expansion formula, we propose a numerical procedure for solving differential equations with fractional derivative by transforming the original system into a system of ordinary differential equations of the first order. Our method is different from the widely used method of L. Yuan and O. P. Agarwal [J. Vib. Acoust. 124, 321–324 (2002)] and overcomes difficulties in satisfying the initial conditions that where noted by A. Schmidt and L. Gaul [Mech. Res. Commun. 33, No. 1, 99–107 (2006; Zbl 1192.74153)]. We tested our procedure on several examples. The results show good agreement with the results obtained by other methods.

65N99 Numerical methods for partial differential equations, boundary value problems
26A33 Fractional derivatives and integrals
Full Text: DOI
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