Novel results for two families of multivalued dominated mappings satisfying generalized nonlinear contractive inequalities and applications

In this manuscript, we prove new extensions of Nashine, Wardowski, Feng-Liu, and Ćirić-type contractive inequalities using orbitally lower semi-continuous functions in an orbitally complete -metric space. We accomplish new multivalued common fixed point results for two families of dominated set-valued mappings in an ordered complete orbitally -metric space. Some new definitions and illustrative examples are given to validate our new results. To show the novelty of our results, applications are given to obtain the solution of nonlinear integral and fractional differential equations. Our results expand the hypothetical consequences of Nashine et al. ( , Nonlinear Anal. Model. Control. 26 (2021), no. 3, 522–533) and Rasham et al. ( , J. Fixed Point Theory Appl. 20 (2018), no. 1, Paper No. 45).