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On the Solvability of Quadratic Multi-Term Hybrid Equation with Nonlocal Hybrid Condition in Banach Algebra Spaces

International Journal of Analysis and Applications | 2026

Paper Details

Authors: Al-Issa S.M.; El-Sayed A.M.A.; Kaddoura I.H.; Al-Sehly R.M.

DOI: 10.28924/2291-8639-24-2026-25

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

This paper investigates the existence of solutions for a class of multi-term hybrid functional equations subject to nonlocal and fractional conditions. We first establish sufficient conditions to ensure the existence of at least one continuous solution by applying Dhage’s fixed-point theorem within an appropriate Banach algebra framework. Subsequently, we extended the analysis to integrable solutions in the Lebesgue space L1 (J, R) under Carathéodory-type growth conditions. The uniqueness of solutions is then addressed by imposing Lipschitz-type constraints on nonlinear and hybrid terms. Furthermore, we examine the continuous dependence of solutions on initial data and parameters. Several illustrative examples are presented to demonstrate the applicability and validity of the obtained results. The theoretical framework developed here unifies and generalizes various existing results for hybrid and nonlocal fractional differential equations. © 2026 the author(s).

Keywords

continuous dependence; Dhage’s fixed-point theorem; fractional derivatives; integrable solutions; multi-term hybrid functional equations; nonlocal conditions; uniqueness