A New Integral Transform for Solving Integral and Ordinary Differential Equations

Abstract

In this research paper, we introduce a new transform belonging to the class of Laplace transforms, called the Yasser-Jassim Transform (YJ 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 and integral 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.

Keywords

• integral transform
• linear differential equation
• integral equation
• voltera equation
• voltera-integro equation