Stability of linear differential equation of higher order using Mahgoub transforms

Abstract

In this paper, by applying Mahgoub transform, we show that the \(n^{\rm th}\) order linear differential equation \[x^{(n)}(v)+\sum_{\kappa=0}^{n-1}a_\kappa x^{(\kappa)}(v)=\psi(v)\] has Hyers-Ulam stability, where \(a_\kappa\)'s are scalars and \(x\) is an \(n\) times continuously differentiable function of exponential order.