Qualitative Analysis of Integro-Differential EquationInvolving a Generalized Caputo Fractional Operator (European Journal of Pure and Applied Mathematics, 2026)
In this study, we investigated the existence and uniqueness of solutions for integro-fractional differential equations with a generalized Caputo operator involving boundary conditions. Utilizing the fixed-point technique, we examined the existence of a solution, and the Banachcontraction technique was employed to determine the uniqueness of the solutions. Moreover, the stability conditions of the Ulam-Hyers are discussed. Subsequently, a suitable application is given to illustrate the validity of this work. The findings presented in this study serve to expand and generalize the existing body of knowledge about nonlocal and classical fractional differential equations.
Keywords: Integro-di erential equation; Fixed point technique; Existence and uniqueness of solutions; Stability result; Generalized fractional derivative