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Application of Sumudu and double Sumudu transforms to Caputo-fractional differential equations. (English) Zbl 1260.34013
Summary: The definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [G. K. Watugala, Int. J. Math. Educ. Sci. Technol. 24, No. 1, 35–43 (1993; Zbl 0768.44003); Math. Eng. Ind. 8, No. 4, 293–302 (2002; Zbl 1025.44003); S. Weerakoon, Int. J. Math. Educ. Sci. Technol. 25, No. 2, 277–283 (1994; Zbl 0812.35004)]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems.

MSC:
34A08 Fractional ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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