Sumudu transform fundamental properties investigations and applications.

By Fethi Bin Muhammad Belgacem, A. A. Karaballi. 2006

380 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6b8a806099b043c83edcec62f2e198d397cac5b2

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In Applied Mathematics

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In Numerical Analysis

Citations in the corpus

Application of He's Homotopy Perturbation Method to Sumudu Transform (2007, background): “[27-29], The Sumudu transform has very special and useful properties and can”
The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method (2013, methodology): “When we take the inverse Sumudu transform of (22) by using the inverse transform table in [11], we get the analytical solution of (20) by STM as follows:”
AN APPLICATION OF THE DOUBLE SUMUDU TRANSFORM (2007, methodology): “Having scale and unit-preserving properties, the Sumudu transform may be used to solve intricate problems in engineering mathematics and applied sciences [ 10 ] without resorting to a new frequency domain.”
The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms (2017, background): “[5, 6] Hindawi Mathematical Problems in Engineering Volume 2017, Article ID 1762729, 8 pages https://doi.”
Sumudu Decomposition Method for Nonlinear Equations (2012, background): “For further detail and properties of this transform, see [10-12].”
Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations (2011, background): “For further detail and properties of this transform, see [47-49].”
Homotopy Analysis Sumudu Transform Method for Nonlinear Equations (2012, neutral): “For further detail and properties of this transform, see [2,4,5].”