Beyond Classical Metrics: Fixed Point Dynamics in tvs-Valued Cone Suprametric Spaces with Fractional Differential Applications

The main aim of this work is to introduce the notion of a tvs-valued cone suprametric space,which unifies and generalizes cone suprametric spaces, tvs-valued cone metric spaces, and cone metric spaces, and to establish new fixed point theorems for single-valued and multivalued generalized contractive mappings within this framework. The presented results extend and unify some well-known outcomes available in the existing literature. To demonstrate the applicability and significance of the proposed theory, a number of illustrative examples are provided. In addition, the obtained fixed point results are employed to investigate the existence of solutions for a Caputo fractional differential equation as well as a Volterra–Fredholm integral equation.