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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.

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