Objectives In this paper we introduce fixed point theorems for generalized rational type $$\alpha$$ α -admissible contractive mappings in partially ordered b-metric spaces and prove the existence and uniqueness of fixed points for self-mappings satisfying the established theorems. Finally, we provide examples in support of our main findings in the setting of partially ordered b-metric spaces. Result New fixed point results have been obtained for generalized rational type $$\alpha$$ α -admissible contractive mappings in the setting of partially ordered b-metric space and we applied one of our results to determine a solution to an integral equation.