Sumudu transform fundamental properties investigations andapplications

Abstract

The Sumudu transform, whose fundamental properties are presented in this paper, is still not widely known, nor used. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. In 2003, Belgacem et al. have shown it to be the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving. Here, using the Laplace-Sumudu duality (LSD), we avail the reader with a complex formulation for the inverse Sumudu transform. Furthermore, we generalize all existing Sumudu differentiation, integration, and convolution theorems in the existing literature. We also generalize all existing Sumudu shifting theorems, and introduce new results and recurrence results, in this regard. Moreover, we use the Sumudu shift theorems to introduce a paradigm shift into the thinking of transform usage, with respect to solving differential equations, that may be unique to this transform due to its unit-preserving properties. Finally, we provide a large and more comprehensive list of Sumudu transforms of functions than is available in the literature.

Implementation and Convergence Analysis of Homotopy Perturbation Coupled With Sumudu Transform to Construct Solutions of Local-Fractional PDEs

“…Some fundamental properties of this transform were introduced and investigated by Belgacem [31]. Katatbeh and Belgacem [32] put into practice this method to get solutions for fractional differential equations.…”

Application of Homotopy Perturbation Sumudu Transform Method for Solving Nonlinear Fractional Heat-like Equations

“…And, various methods are also combined with the Sumudu transformation method, such as the homotopy analysis Sumudu transform method [20], which is a combination of the homotopy analysis method and the Sumudu transformation method. Another example is the Sumudu decomposition method [21,22], which is a combination of the Sumudu transform method and the Adomian decomposition method.…”

On Image Formulae Leading to Fractional Kinetic Equations Solutions via Sumudu Generalized k-Bessel Functions

“…For more details about Sumudu transform, see ( [1][2][3][4][5][6][7][8][9]). The Sumudu transform over the set functions…”