The stability of nonlinear delay integro-differential equations in the sense of Hyers-Ulam-Reference-Cited by-同舟云学术

The stability of nonlinear delay integro-differential equations in the sense of Hyers-Ulam

Published:2023-01-01 Issue:1 Volume:10 Page:
ISSN:2353-0626
Container-title:Nonautonomous Dynamical Systems
language:en
Short-container-title:

Author:

Graef John R.¹,Tunç Cemil²,Şengun Merve²,Tunç Osman³

Affiliation:

1. Department of Mathematics, University of Tennessee at Chattanooga , Chattanooga , TN 37403 , USA

2. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus , 65080 Van , Turkey

3. Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Campus , 65080 Van , Turkey

Abstract

Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on a finite interval was considered. The nonlinear term in the equation contains multiple time delays. In addition to giving some new theorems on the existence and uniqueness of solutions to the equation, the authors also prove the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the equation. The proofs use several different tools including Banach’s fixed point theorem, the construction of a Picard operator, and an application of Pachpatte’s inequality. An example is provided to illustrate the existence, uniqueness, and stability properties of solutions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/msds-2022-0169/pdf

Reference22 articles.

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