Existence and uniqueness of solutions for random fuzzy fractional integral and differential equations

Abstract

In this paper the random fuzzy fractional integral and differential equations are introduced. Under Lipschitz condition we obtain the existence and uniqueness theorems of solutions for two general forms of random fuzzy fractional integral equations. To prove this assertion we use an idea of successive approximations. Moreover, the approach is followed to prove the existence and uniqueness of solutions for random fuzzy fractional initial value problem under Caputo-type fuzzy fractional derivatives. The method is illustrated by solving an example.