Applications of Fixed Point Results to Fractional Differential and Nonlinear Mixed Volterra–Fredholm Integral Equations

This work aims to introduce the concept of graphic rational contractions in the framework of extended F-metric spaces and to establish fixed point theorems related to these mappings. In addition, we define and examine the class of interpolative Ćirić–Reich–Rus-type cyclic contractions in the same setting, deriving several new fixed point results that broaden existing theories. To illustrate the validity and originality of the obtained results, appropriate examples are presented. Furthermore, the developed theoretical results are applied to study the existence of solutions for fractional differential equations and nonlinear mixed Volterra–Fredholm integral equations, highlighting their effectiveness and practical importance.