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New method for solving linear fractional differential equations. (English) Zbl 1239.34007
Summary: We extend the Mittag-Leffler Function method to solve linear differential equations with fractional order. A solution is constructed in a power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
34A30 Linear ordinary differential equations and systems, general
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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