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 (<sub>0</sub>D<sub>x</sub><sup>β</sup>y)'(x) = b(x)y(x), where (<sub>0</sub>D<sub>x</sub><sup>β</sup>y)(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.