Qualitative Results for Nonlinear Integro-Dynamic Equations Via Integral Inequalities

Abstract

In this paper, a nonlinear integro-dynamic equation on time scales with local initial condition is considered. The purpose of this paper is to prove existence and uniqueness of solutions and to investigate qualitative properties of solutions of this equation such as boundedness, dependence of solutions on initial conditions, functions, and parameters, and Ulam stability. The analysis is based on the Krasnoselskiĭ fixed point theorem and Gronwall-type dynamic inequalities. For the illustrative purpose of our main results, examples on a nonstandard time scale domain are provided.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Dependence of Solutions; Existence and Uniqueness; Gronwall Inequality; Hyers-Ulam Stability; Hyers-Ulam-Rassias Stability; Integro-Dynamic Equations; Time Scales

International Standard Serial Number (ISSN)

1662-3592; 1575-5460

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2022 Springer, All rights reserved.

Publication Date

01 Dec 2022

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