BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: <inline-formula><tex-math id="M1">$ {\mathbb J} $</tex-math></inline-formula>-TRANSFORM PROPERTIES AND APPLICATIONS

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 transform 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 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 J-transform in addressing those limitations.