On the concept of solutions for fuzzy fractional initial value problem

Abstract

It is evident that fuzzy arithmetic is different than that of normal arithmetic due to the different classes of functions and symbols. This article is concerned with an appropriate definition of the fractional derivative and integral in a fuzzy sense and a new concept of solutions for a fuzzy Caputo fractional initial value problem (IVP) is presented. Further, under some sufficient conditions on IVP, the existence, uniqueness, and stability results of the solution are established by applying the iterate methods. For the validation of established results, a particular fuzzy fractional Riccati differential equation is presented.