Some Properties and Applications of a New General Triple Integral Transform "Gamar Transform"

Abstract

The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current transform to a number of existing triple integral transforms such as those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties and prove some important results, including linearity property, existence theorem, triple convolution theorem, and derivatives properties. Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. The capacity of general triple integral transforms to change PDEs into simple algebraic equations is demonstrated.