# Solving An Initial Value Problem

Recently, the issue of fuzzy fractional calculus and fuzzy fractional differential equations has emerged as the significant subject, and this new theory has become very attractive to many scientists.

In this section, we present basic notations and necessary preliminaries used throughout the paper.Using some recent results of fixed point of weakly contractive mappings on the partially ordered space, the existence and uniqueness of solution for interval fractional delay differential equations (IFDDEs) in the setting of the Caputo generalized Hukuhara fractional differentiability are studied.The dependence of the solution on the order and the initial condition of IFDDE is shown.\end\displaystyle \end$$ is the unique solution to (3.1).□ The conclusion of Theorem 3.1 is still valid if the existence of a w-monotone lower solution for problem (3.1) is replaced by the existence of a w-monotone upper solution for problem (3.1).

Interval-valued delay fractional differential equation: Let us consider again the interval-valued delay fractional differential equation with Caputo generalized Hukuhara fractional differentiability under the form has a unique fixed point. □ In the following corollary, we analyze the dependence of the solution on the order and the initial condition for problem (3.6).