Work

On the Existence of Solutions for ψ-Caputo Fractional Integro-Differential Boundary Value Problems

Year: 2026

Type: article

Abstract: In this article, we investigate the existence of solutions for a class of fractional integro-differential equations (FIDE’s) involving the ψ-Caputo fractional derivative (ψ-CFD) subject to ψ-Caputo boundary conditions. The analysis is carried out in an appropriate Banach space setting using the Mönch fixed-point theorem. Furthermore, sufficient conditions ensuring the existence and uniqueness of solutions are derived by employing tools from nonlinear functional analysis. In addition, the obtained results contribute to the current literature by extending existing works on fractional differential equations (FDE’s) involving generalized Caputo-type operators. The novelty of this study lies in the incorporation of ψ-CFD’s together with ψ-Caputo boundary conditions under the framework of Mönch fixed-point theory. An illustrative example is provided to verify the applicability and effectiveness of the theoretical findings.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10050348

Authors: Panjaiyan Karthikeyan, Ambigapathi Manikandan, Mohammed Rabih, Marappan Sathish Kumar

Institutions: Qassim University, Paavai Engineering College

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Qassim University