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

Abstract

Abstract 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 $\mathcal{Z}$ -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.

Keywords

• q-ROF sets
• q-ROF mapping
• Hybrid q-ROF Z $\mathcal{Z}$ -contraction