Rida-Jassim integral transform: a tool for solving linear and non-linear differential equations

Abstract

In this paper, we introduce a new integral transform belonging to the class of Laplace transforms, called the Rida-Jassim Transform (RJ Transform). We explore its properties and compare it to the classical Laplace transform. Furthermore, we provide proofs for the key properties associated with this transform and demonstrate its application in solving differential equations. By employing this new transform, we can reduce the original problem to an algebraic equation that can be solved directly, followed by applying the inverse transform to obtain the solution to the original problem.