Theaim of this research is to establish existence and uniqueness results for the Riemann–Liouville fractional integral equation of order $\alpha$$\varkappa \left(t\right)=f\left(t\right)+{\displaystyle \frac{\lambda }{\Gamma \left(\alpha \right)}}\underset{0}{\overset{t}{\int }}{\left(t-s\right)}^{\alpha -1}g\left(s,\varkappa \left(s\right)\right)ds,t\in [0,1],$ by developing common fixed point theorems for generalized contractions involving control functions of two variables in the framework of complex valued suprametric spaces. The proposed results extend and generalize several existing findings in the literature, and some illustrative examples are provided to demonstrate the novelty and applicability of the main theorem.

This work aims to introduce the concept of graphic rational contractions in the framework of extended $\mathcal{F}$-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.

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.