Shehu Integral Transform and Hyers-Ulam Stability of nth order Linear Differential Equations

In this paper, we establish the Shehu transform expression for homogeneous and non -homogeneous linear differential equations. With the help of this new integral transform, we solve higher order linear differential equations in the Shehu sense. Moreover, this pa-per introduced a new concept to find the Hyers-Ulam stability of the differential equation. This is the first attempt to use the Shehu transform to prove the Hyers-Ulam stability of the differential equation. Finally, the applications and remarks are discussed to demon-strate our strategy. Applications of the Shehu transform to fractional differential equations, Newton's law of cooling, and free undamped motion are also discussed.(c) 2022 The Author(s). Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative.This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )