Toward the existence of solutions of fractional sequential differential equations with uncertainty

The main study of this paper is focused on the solutions of a class of fuzzy sequential fractional differential equations in the form of (0Dx^βy)′(x) = b(x)y(x), where (0Dx^βy)(x) is the fuzzy Riemann-Liouville derivative of order β ∈ (0, 1). On this subject, a new fuzzy complete metric space is introduced. Finally, we proof the existence and uniqueness of our solution using the contraction principle.