Existence and Uniqueness Results Using Interactive Fuzzy Fractional Derivative

Abstract

This study describes the use of an interactive derivative of Caputo to a fuzzy fractional starting value issue. The beginning setting of the equation is represented by a fuzzy subset, and the differentiation is indicated by $ F $-correlated derivative. In first we provide new and essentials theorems related to $ F $-derivative of order $\alpha \in (0, 1]$. Secondly we use these theorems to extract the mild solution of the main problem. Thirdly we demonstrate the uniqueness of solutions by the Schauder fixed point theorem. Lastly, a case study is given to exhibit the correctness of the acquired outcomes.