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BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: J-TRANSFORM PROPERTIES AND APPLICATIONS
Shehu Maitama,Weidong Zhao
Keywords:Laplace transform, Sumudu transform, natural transform, Elzaki transform, ordinary and partial differential equations.
Abstract:
      In this paper, we introduce an efficient integral transform called the J-transform which is a modification of the well-known Sumudu transform and the natural transform for solving differential equations with real applications in applied physical sciences and engineering. The J-transform is more advantageous than both the Sumudu and the natural transform. Interestingly, our proposed J-transform can be applied successfully to solve complex problems that are ordinarily beyond the scope of either Sumudu or natural transform. As a proof of concept, we consider some classic examples and highlight the limitations of the previously reported integral transforms and lastly demonstrate the superiority of the proposed J-transform in addressing those limitations.