In this paper, we introduce the notion of generalized (α, ϕ, ψ) - Geraghty contractive type mappings in the setup of Sb-metric spaces and α-orbital admissible mappings with respect to ϕ. Furthermore, the fixed-point theorems for such mappings in complete Sb-metric spaces are proven without assuming the sub-additivity of ψ. Some examples are provided for supporting of our main results. Also, we gave an application to integral equations as well as Homotopy. 2000 Mathematics Subject Classification. 54H25, 47H10, 54E50.