Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers

Abstract

In this paper, we consider a conformable fractional diferential equation with a constant coefcient and obtain an approximation for this equation using the Radu–Mihet method, which is derived from the alternative fxed- point theorem. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers–Ulam-H-Fox stability for this equation. Finally, by providing numerical examples, we show the application of the obtained results.