Applications of contractive-like mapping principles to fuzzy fractional integral equations with the kernel $$\psi $$-functions

Abstract

In this work, we present a new class of generalized fractional integral equations with respect to the kernel $$\psi $$ -function under the fuzzy concept. The results of this problem can be used to recover a wide class of fuzzy fractional integral equations by the choice of the kernel $$\psi $$ -function. Without the Lipschitzian right-hand side, we investigate the existence and uniqueness of the fuzzy solutions by employing the fixed point theorem of weakly contractive mappings in the partially ordered space of fuzzy numbers. The proposed approach is based on the concept of a fuzzy metric space endowed with a partial order and the altering distance functions. In addition, the continuous dependence of solutions on the order and the initial condition of the given problem is also shown. Some concrete examples are presented in order to consolidate the obtained result.