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The aim of this paper is to introduce new concepts of α-η-complete metric space and α-η-continuous function and establish fixed point results for modified α-η-ψ-rational contraction mappings in α-η-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for ψ-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.