In this paper, we introduce and define a new metric on the space of fuzzy continuous functions in the fractional calculus. Regarding this metric and using the well-known Banach fixed point theorem, we provide some conditions that guarantee the existence and uniqueness of solution to a nonlinear fuzzy fractional differential equation in the proposed metric. Finally, two examples are given to illustrate the results.

Tbilisi Mathematical Journal, Vol. 10(1) (2017), pp. 197-205