Qualitative Analysis of Quaternion Fuzzy Fractional Differential Equations with Ξ-Hilfer Fractional Derivative

Abstract

In this work, we discuss the existence and stability of solution for a quaternion fuzzy fractional differential equation in the generalized regular fuzzy function space with Ξ-Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Second of all, we give our first existence result, based on fixed point theorem and to deal with the uniqueness result. Next, this article is devoted to the investigation of the stability results. We employed a version of Piccard operator theorem to study the stability in the sense of Ulam-Hyers. In the end, we provide a couple of examples to illustrate our results.