Introducing and Analyzing Deeper Sumudu Properties

Abstract

The Sumudu Transform, herein simply referred to as the Sumudu, was previously firmly established by the author et al.[2003/2005] as the theoretical dual to the Laplace Transform, where from the Laplace-Sumudu Duality (LSD). In fact, due to its units and scale preserving properties, in many instances, the Sumudu may be preferred to its dual for solving problems in engineering mathematics, without leaving the initial argument domain. Many fundamental Sumudu properties were presented in the literature, by this author and others. Aside from reestablishing these with alternative tools, essentially deeper Sumudu properties and connections are analyzed, and new results are presented. As such, this paper attempts to be the single most comprehensive source about the Sumudu Transform properties, up to date.