On the Existence of Solutions for Atangana–Baleanu Type Fractional Integral Equations via Fixed Point Theorems in Extended F-Metric Spaces

The primary objective of this research article is to investigate the concept of extended (Formula presented.) -metric spaces and to establish a series of fixed point theorems for generalized contractions within this framework. We further introduce and analyze the notion of interpolative Kannan-type cyclic contractions in extended (Formula presented.) -metric spaces, deriving several novel fixed point results associated with these mappings. In addition, we obtain common fixed point theorems for rational contractions, thereby extending and unifying a variety of existing results available in the literature. To highlight the novelty and effectiveness of the proposed results, several illustrative examples are provided. Moreover, the theoretical findings are successfully applied to the solution of Atangana–Baleanu fractional integral equations as well as Volterra integral equation of Hammerstein type, demonstrating their practical significance and wide-ranging applicability.