Adapting a new formula to generalize multidimensional transforms

Abstract

In this article, we present a new general formula of a multidimensional general integral transform; this new formula covers mostly all types of multi‐integral transforms of the Laplace class. Moreover, single, double, and triple integral transforms of the Laplace kind can be derived from the proposed formula. So, the obtained results in this study can be utilized to reduce computations when using these transforms of same category in other studies. Fundamental properties of the new transform, including linearity, uniqueness, and the inverse, are introduced. In addition, we establish the multi‐convolution theorem and some important results related to partial derivatives. To show the applicability of new multidimensional transform, we employ the new proposed transform to investigate the solutions of some partial differential equations and partial integro‐differential equations.