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 ? ? (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.