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Volume 10, Number 4, 2020, Pages 1223-1241                                                                DOI:10.11948/20180258
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.
      In this paper, we introduce an efficient integral transform called the ${\mathbb J}$-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 ${\mathbb J}$-transform is more advantageous than both the Sumudu transform and the Natural transform. Interestingly, our proposed ${\mathbb J}$-transform can be applied successfully to solve complex problems that are ordinarily beyond the scope of either Sumudu transform 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 ${\mathbb J}$-transform in addressing those limitations.
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