Theoretical Analysis of Uniqueness and Stability for Nonlinear Fractional Volterra–Fredholm Systems

Abstract

The primary goal of this research is to investigate the Hyers-Ulam stability (HUS) and Hyers-Ulam-Rassias stability (HURS) for impulsive Volterra-Fredholm system. The uniqueness
of solutions for the proposed system are investigated using fixed-point technique (FPT).
We further investigate the HUS and HURS using generalized Gronwall inequality alongside Picard’s operator technique of the equation under the Caputo fractional derivative by
establishing appropriate adequate conditions. Finally, numerical application is shown to demonstrate the stability of the proposed system.