Stability of linear differential equation of higher order using Mahgoub transforms

Volume 30, Issue 1, pp 1--9 https://doi.org/10.22436/jmcs.030.01.01

Publication Date: November 25, 2022 Submission Date: July 14, 2022 Revision Date: August 07, 2022 Accteptance Date: August 18, 2022

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Authors

R. Murali - Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635 601, Tamil Nadu, India. A. Ponmana Selvan - Department of Mathematics, Kings Engineering College, Irungattukottai, Sriperumbudur, Chennai-602 117, Tamil Nadu, India. S. Baskaran - Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635 601, Tamil Nadu, India.

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.

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Keywords

• Hyers-Ulam stability
• linear differential equations
• Mahgoub transform

MSC

•  34K20
•  26D10
•  44A05
•  39B82

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