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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.

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