Multivalued Hardy-Rogers type ЗΘ-contraction and generalized simulation functions

Abstract

The purpose of this paper is to introduce the notion of multivalued Hardy-Rogers ??-contraction in the sense of generalized simulation functions and to present the corresponding fixed point results with some examples. Moreover, we study the strict fixed point and well-posedness, data dependence, as well as, the Ulam-Hyres stability of the fixed point problem. As an application, we prove the existence of the solution for nonlinear fractional differential equation involving Caputo fractional derivative.