Toward the Existence of Solutions of Fractional Sequential Differential Equations With Uncertainty

Abstract

The main study of this paper is focused on the solutions of a class of fuzzy sequential fractional differential equations in the form of (D-0(x)beta y)' (x) = b(x)y(x), where (D-0(x)beta y) (x) is the fuzzy Riemann-Liouville derivative of order beta is an element of(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.