The formal balls in fuzzy normed space (characterized by closed balls in) are ordered by reverse inclusion depending on the concept of level sets. The set of formal balls in a fuzzy normed space is called a fuzzy domain normed space denoted by. This set is directed complete partially ordered set (dcpo), its maximal elements are the suprema. A contraction mapping principle is defined on. Banach fixed point theorem is studied and proved on .

The main objective of this paper is to state and prove the existence and uniqueness theorem of fractional differential equations using one of the most important theorems in nonlinear functional analysis which is the Sadoviski fixedpoint theorem. Here the undertaken differential operator is in the sense of Riemann-Liouville definition of fractional integration.