Mittag-Leffler-Hyers-Ulam stability of Euler-Cauchy differential equation using Laplace transform

Abstract

In this paper, we study the Mittag-Leffler-Hyers-Ulam stability and MittagLeffler-Hyers-Ulam-Rassias stability of the Euler-Cauchy differential equation using Laplace transform. Basically, for the first time, the Mittag-Leffler-Hyers-Ulam stability of second order differential equation with variable coefficients has been studied through the Laplace transforms. We develop this approach to identify the necessary conditions that the eigenvalue Sturm-Liouville equation is Mittag-Leffler-Hyers-Ulam stable.