FUZZY INITIAL VALUE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATION ON LINEAR CORRELATED FUZZY FUNCTION SPACE

Abstract

The paper focuses on linear correlated fuzzy function space
( ) A with its special properties . Firstly, we show some special properties of the norm operator on two spaces ( ) ( 2) 1 ,
A A with A kA 2 1  , A A 1 2 , given fuzzy numbers. Besides, we study the fractional differential equation in the space ( ) A . By combining the special properties of space with fractional order calculations and the fixed point theorem, we have built assumptions to ensure that the problem has unique solution.