Existence, Uniqueness and HU-Stability Results for Nonlinear Fuzzy Fractional Volterra-Fredholm Integro-Differential Equations

Abstract

In this paper, we established some new results concerning the existence and uniqueness of the solutions of nonlinear Atangana-Baleanu-Caputo fractional (ABC-fractional) Fuzzy Volterra-Fredholm integro-differential equations. These new findings are obtained using the theorems of a fixed point. In addition, we investigate Hyers-Ulam stability for this fractional system. Our work extends and improves the results in the literature. Finally, some examples demonstrate the validity of the obtained theoretical results.

On a New Class of Impulsive η-Hilfer Fractional Volterra-Fredholm Integro-Differential Equations

“…This justifies the usage of and generalization of the fractional integro-differential equations, Existence, uniqueness and stability [16], Uniqueness and stability results for Caputo type [12], existence results on Hadamard neutral [15], controllability [14], On time scales [13], existence and uniqueness [11], uniqueness [20], existence and stability results [34], β-Ulam-Hyers stability [42], existence and stability results for ψ-Hilfer [41], existence results for Hilfer [40], existence results of Katugampola type [25], existence and stability of solutions of ψ-Hilfer [22], existence and stability of ℜ-Hilfer [17]. Using Hilfer operators, several scholars have recently looked into the uniqueness, existence, stability, and generalization of different BVPs [26].…”

“…. We will examine the expression (14) for the value p ∈ (1, 2). Theorem 3.1 allows us to conclude that:…”

Non-Instantaneous Periodic BVP of Fractional Volterra-Fredholm Models

“…For instance, the transit of drugs through the circulation occurs gradually and continuously. On the other hand, non-instantaneous impulse models help clarify these problems, [8,9,10,13]. Therefore, by using fixed point theory, various researchers have looked into some existence and uniqueness conclusions for nonlinear IDEs of fractional order, [7,8,11].…”