Abstract
By combining the results of Wardowski's cyclic contraction operators and admissible multi -valued mappings, the motif of eta-cyclic (alpha(*), beta(*))-admissible type F-contraction multivalued mappings are presented. Moreover, some novel fixed point theorems for such mappings are proved in the context of Mb-metric spaces. Also, two examples are given to clarify and strengthen our theoretical study. Finally, the existence of a solution of a pair of ordinary differential equations is discussed as an application.