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F. B. M. Belgacem, A. A. Karaballi and S. L. Kalla, “Analytical Investigations of the Sumudu Transform and Applications to Integral Production Equations,” Mathematical Problems in Engineering (MPE), Vol. 2003, No. 3, 2003, pp. 103-118.

has been cited by the following article:

• TITLE: Laplace Transform Analytical Restructure

  AUTHORS: Fethi Bin Muhammad Belgacem, Rathinavel Silambarasan

  KEYWORDS: Laplace Transform; Natural Transform; Sumudu Transform

  JOURNAL NAME: Applied Mathematics, Vol.4 No.6, June 14, 2013

  ABSTRACT: In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation of the original function. Various analytic consequent results are given. The simplicity and efficacy of the method are illustrated through many examples with shown Maple graphs, and transform tables are provided. Finally, a new infinite series representation related to Laplace transforms of trigonometric functions is proposed.