Ulam stability and solution behavior of implicit fractional Volterra-Fredholm equations via generalized Hilfer-Katugampola calculus

This article investigates the existence, uniqueness, and stability of solutions for a class of nonlinear implicit fractional Volterra-Fredholm integro-differential equations involving the Hilfer-Katugampola fractional derivative. Employing the Banach fixed-point theorem, we establish sufficient conditions for the problem’s well-posedness and prove Ulam-Hyers stability results through Grönwall’s inequality. The theoretical framework is complemented by numerical simulations, where an illustrative example is solved using both analytical methods and computational techniques. The numerical results demonstrate strong agreement with the theoretical predictions, confirming the robustness of our approach. This combined analysis provides a comprehensive foundation for studying such fractional integro differential equations, highlighting their structural properties while verifying solution behavior through practical implementation.