Multi-Term Nonlinear Fractal-Orders Delayed Abel Integral Equation: Existence of Solutions, Stability, and Applications

Authors

Ahmed M. A. El-Sayed Faculty of Science, Alexandria University, Alexandria, Egypt https://orcid.org/0000-0001-7092-7950
Hanadi Zahed Department of Mathematics, College of Science, Taibah University, Saudi Arabia https://orcid.org/0009-0008-7020-0450
Shaymaa I. Nasim Faculty of Science, Alexandria University, Alexandria, Egypt
Eman M. A. Hamdallah Faculty of Science, Alexandria University, Alexandria, Egypt

DOI:

https://doi.org/10.37256/cm.6620258293

Keywords:

Abel integral equation, existence of solutions, delay integral equation, fractal operators, continuous dependence, Hyers-Ulam stability, nonlocal-integral problems

Abstract

In this paper we study a multi-term non-linear fractal orders delayed integral equation of the second kind. We examine the existence of integrable solution x ∈ L₁[0, T]. Under certain assumptions, the uniqueness of this solution will be demonstrated. Additionally, the continuous dependence on the problem’s parameters will be investigated. The Hyers-Ulam stability of the problem itself will be established. Finally, as applications we study two initial value problems of multi-term fractal orders integro-differential equations.

Downloads

Published

2025-11-09

Issue

Contemporary Mathematics, Volume 6 Issue 6 (2025)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.