In this article, we study Feng-Liu [Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), 103–112.] type fixed point theorems and present some new results for multi-valued mappings in metric spaces using the concept of ω-distance. We also discuss, some non-trivial examples to illustrate facts. Finally, we present applications of our results to integral inclusions and non-linear matrix equations. An example is given, together with convergence and error analysis, as well as average CPU time analysis and visualization of solution in surface plot.