The aim of this paper is to use the concept of the generalized H-derivative to define fuzzy Caputo’s H-derivative of order β ∈(1,2]. Our definition is an extension of fuzzy Caputo’s H-derivative of order β ∈(0,1] and higher order H-derivative of integerorder. After that, we study fuzzy fractional initial value p roblems of order β ∈(1,2] and give an algorithm to solve them based onthe characterization theorem. Finally, we apply the reprod ucing kernel Hilbert space method to obtain approximate solutions of second order fuzzy fractional initial value problems and give some numerical examples.