Hyers-Ulam-Rassias stability of abstract second-order linear dynamic equations on time scales

Volume 24, Issue 2, pp 110--118 http://dx.doi.org/10.22436/jmcs.024.02.02

Publication Date: January 18, 2021 Submission Date: October 23, 2020 Revision Date: November 05, 2020 Accteptance Date: November 16, 2020

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Authors

Maryam Alghamdi - Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia. Alaa Aljehani - Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia. Alaa E. Hamza - Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.

Abstract

In this paper, we obtain new sufficient conditions for Hyers-Ulam and Hyers-Ulam-Rassias stability of abstract second-order linear dynamic equations on time scales. Also a new sufficient condition for the existence and uniqueness of solutions is established, via Banach's fixed point theorem. Finally, two illustrative examples are given to demonstrate the applicability of the theoretical results.

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Keywords

• Linear dynamic equations on time scales
• Hyers-Ulam stability
• Hyers-Ulam-Rassias stability

MSC

•  34D20
•  34N05
•  39A30

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