**Abstract**

In this paper, the Cauchy problem of fuzzy fractional differential equations *Tγu t*ðÞ¼ *F t*ð Þ , *u t*ð Þ , *u t*ð Þ¼ <sup>0</sup> *u*0, with fuzzy conformable fractional derivative (*γ*-differentiability, where *γ* ∈ ð �Þ 0, 1 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*.

**Keywords:** fuzzy conformable fractional derivative, fuzzy fractional differential equations, existence and uniqueness of solution, approximate solutions, Cauchy problem of fuzzy fractional differential equations
