Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions

In the present article, we have introduced the notions of γ -admissibility for the pair of q -ROF set-valued maps and admissible hybrid q -ROF Z Z -contraction. Notions introduced in the article generalizes the existing concepts in fuzzy literature. Common fixed point result for a pair of γ -admissible q -ROF mappings in b -metric spaces utilizing the introduced contraction is presented. A nontrivial example to support the obtained results is also included. As an application, we have discussed the existence of solution of system of non-linear n -th order differential inclusions with non-local and integral boundary conditions.