In this paper, we introduce the concept of a generalized alpha-Suzuki-Geraghty type contraction mapping and obtain fixed point results in the framework of an f-orbitally complete b-metric space. The results proved herein improve, generalize, and unify various comparable results in the existing literature. Some examples are presented to validate the effectiveness and applicability of our main result. It is also shown that the presented results are proper extensions of corresponding results in the existing literature. As an application of our obtained result, we establish the existence of a solution of integral equations in the setup of b-metric spaces.