Existence, Uniqueness and Approximate Solutions of Fuzzy Fractional Differential Equations

Abstract

In this paper, the Cauchy problem of fuzzy fractional differential equations Tγut=Ftut, ut0=u0, with fuzzy conformable fractional derivative (γ-differentiability, where γ∈01) are introduced. We study the existence and uniqueness of solutions and approximate solutions for the fuzzy-valued mappings of a real variable, we prove some results by applying the embedding theorem, and the properties of the fuzzy solution are investigated and developed. Also, we show the relation between a solution and its approximate solutions to the fuzzy fractional differential equations of order γ.