MITTAG-LEFFLER-HYERS-ULAM STABILITY OF EULER-CAUCHY DIFFERENTIAL EQUATION USING LAPLACE TRANSFORM

MITTAG-LEFFLER-HYERS-ULAM STABILITY OF EULER-CAUCHY DIFFERENTIAL EQUATION USING LAPLACE TRANSFORM

A. B. I. Ahmed

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Abstract

In this paper, we study the Mittag-Leffler-Hyers-Ulam stability and Mittag- Leffler-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.

Keywords

Mittag-Leffler-Hyers-Ulam stability, Mittag-Leffler-Hyers-Ulam-Rassias stability, Euler-Cauchy equation, variable coefficients, Laplace transform, Sturm-Liouville equation.