A contractive approach in generalized suprametric spaces with applications to fractional boundary value and epidemiological problems

This manuscript analyzes Reich, Ćirić, and Banach contractions in complete extended suprametric spaces by using the Fw-class of functions. We establish new fixed point theorems for these Fw−contractions, extending classical results in a generalized metric setting. To validate the theoretical results, we construct illustrative examples and support them through both numerical computations and graphical simulations. As practical applications, we employ the Fw−Reich contraction to investigate the existence and uniqueness of solutions to an epidemiological model describing the spread of infectious diseases. Furthermore, the Fw−Banach contraction is utilized to investigate both the existence and uniqueness of solutions for a nonlinear fractional integral boundary value problem. These outcomes extend past classical fixed point theorems not just in the sense that they generalize classical fixed point theorems but also provide a context in which one can deal with weaker contractive conditions (Fw-type contractions) in more general exotic spaces like extended suprametric spaces and allow them to be applied to a wider range of not just nonlinear problems in analysis but applied sciences as well.