BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: $ {\mathbb J} $ -TRANSFORM PROPERTIES AND APPLICATIONS
Weidong Zhao, Shehu Maitama · Journal of Applied Analysis & Computation · 2020
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.