Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint

Author:

El-Sayed Ahmed M. A.1ORCID,Alhamali Antisar A. A.2,Hamdallah Eman M. A.1,Ebead Hanaa R.1ORCID

Affiliation:

1. Faculty of Science, Alexandria University, Alexandria 21521, Egypt

2. Faculty of Science, Al-Zaytoonah University, Bani Walid 38645, Libya

Abstract

This manuscript investigates a constrained problem of an arbitrary (fractional) order quadratic functional integro-differential equation with a quadratic functional integro-differential constraint. We demonstrate that there is at least one solution x∈C[0,T] to the problem. Moreover, we outline the necessary demands for the solution’s uniqueness. In addition, the continuous dependence of the solution and the Hyers–Ulam stability of the problem are analyzed. In order to illustrate our results, we provide some particular cases and instances.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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