Abstract
In this article, some fixed point results satisfying an extended multi-valued F-contraction mapping in the context of metric-like spaces are developed. Also, some standard examples are dressed to support our theoretical consequences. Finally, we conclude our paper with two important applications for the system of functional equations and to find a bounded solution for a class of a Fredholm type integral inclusion. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.