Coincidence fixed point theorem in a Menger probabilistic metric spaces

Abstract

In this paper, we discuss the existence and uniqueness of solutions for a class of multi-term time-fractional impulsive integro-differential equations with state dependent delay subject to some fractional order integral boundary conditions. In our consideration, we apply the Banach, and Sadovskii fixed point theorems to obtain our main results under some appropriate assumptions. An example is given at the end to illustrate the applications of the established results. Fixed point theory of nonexpansive type single valued mappings provides techniques for solving a variety of applied problems in mathematical sciences and engineering. The aim of this paper is to prove the existence of coincidence points, coupled points and common coupled fixed points of nonexpansive type conditions satisfied by single valued maps which include both continuous and discontinuous mappings on Menger probabilistic metric spaces.