Application of Triple ARA Integral Transforms to solving partial differential equations

Abstract

In this paper, we present the development of a novel triple trans- form, termed the triple ARA transform. This transformative approach, specifically designed as a triple-integral transform, proves effective in addressing challenges posed by partial differential equations and vari- ous problem-solving scenarios. Our investigation delves into key char- acteristics of the triple ARA transform, emphasizing aspects such as its existence, linearity, and noteworthy findings pertaining to partial derivatives and the double convolution theorem. The versatility of the triple ARA transform is demonstrated through its application in solving a range of partial differential equations, including but not lim- ited to the homogeneous equation, and non-homogeneous equation in addressing diverse physical phenomena. Our study concludes by af- firming the user-friendly nature of our novel method in comparison to analogous transforms. The triple ARA transform emerges as a valu- able tool for researchers and practitioners seeking efficient solutions to a variety of mathematical and physical problems.