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Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1987) Integrals and Derivatives of Fractional Order and Some of Their Applications. Nauka I Tekhnika, Minsk.

has been cited by the following article:

• TITLE: Sumudu Transformation or What Else Can Laplace Transformation Do

  AUTHORS: Alfred Wünsche

  KEYWORDS: Mellin Transformation, Fractional Integration, Geometric Series and Exponential Series, Error Function, Laguerre Polynomials, Generating Functions of Hermite Polynomials, Bessel Functions, Asymptotic Series, Operator Identities

  JOURNAL NAME: Advances in Pure Mathematics, Vol.9 No.2, February 26, 2019

  ABSTRACT: The transition from a known Taylor series of a known function f(x) to a new function primarily defined by the infinite power series with coefficients f(n)(0)from the Taylor series of the function f(x)can be made by an integral transformation which is a modified Laplace transformation and is called Sumudu transformation. It makes the transition from the Exponential series to the Geometric series and may help to evaluate new infinite power series from known Taylor series. The Sumudu transformation is demonstrated to be a limiting case of Fractional integration. Apart from the basic Sumudu integral transformation we discuss a modification where the coefficients from the Taylor series are not changed to f(n)(0)but only to . Beside simple examples our applications are mainly concerned to calculate new Generating functions for Hermite polynomials from the basic ones.