Existence, uniqueness, and UH-stability results for nonlinear fuzzy fractional Volterra–Fredholm integro-differential equations

Abstract

Abstract In this research, we provide certain novel requirements for the existence and uniqueness of fuzzy solutions for a type of nonlinear fuzzy Caputo fractional generalized Hukuhara Volterra–Fredholm integro-differential equations under integral boundaries. The required findings are demonstrated by employing the Banach and successive iterations convergence technique. First, we give the two analytic form solution equivalent the main equation and then we show the existence and uniqueness of solutions with the help of the successive iterations convergence technique, as well as Banach’s fixed point theorem. Moreover, we examine the generalized Ulam–Hyers (GUH) and Ulam–Hyers–Rassias stability for our main problem. An example is provided to demonstrate the reliability of our findings.