Second order fuzzy fractional differential equations under Caputo's H-differentiability

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