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 bb-metric space. We accomplish new multivalued common fixed point results for two families of dominated set-valued mappings in an ordered complete orbitally bb-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. (Feng–Liu-type fixed point result in orbital b-metric spaces and application to fractal integral equation, Nonlinear Anal. Model. Control. 26 (2021), no. 3, 522–533) and Rasham et al. (Common fixed point results for new Ciric-type rational multivalued-contraction with an application, J. Fixed Point Theory Appl. 20 (2018), no. 1, Paper No. 45).