Introducing a New Integral Transform Called “AR-Transform”

Abstract

In this paper, we have propounded a new integral transform called AR-Transform. AR-Transform stand for “Akbar and Rashid Transform”. We discussed functional characteristics of AR-Transform and obtained AR-Transform of some elementary functions. We also proved theorem of AR-Transform for derivatives of a function. We explore its usefulness in physics, engineering and mathematics, by solving different problems, such as, RL series circuit, Uranium decay model, model of simple harmonic motion and other differential equations to illustrate its power and versatility. Our analysis demonstrates that the AR-Transform is a valuable addition to the existing suite of integral transforms and holds great promise for future research and application.