Fixed Point Theorems for Generalized Rational Type Contractions in Orthogonal Extended b-Metric Spaces with Applications

In this paper, we introduce and study a new class of generalized rational type contractions in the framework of orthogonal extended b-metric spaces. We establish several fixed point theorems for single-valued mappings satisfying various rational type contractive conditions involving a control function and an orthogonal structure. The notion of orthogonal extended -metric space generalizes several existing metric space structures and provides a unified setting for the analysis of fixed point problems. We prove the existence and uniqueness of fixed points under abla-orbital rational type contractions, abla-rational Geraghty type contractions, and abla-rational Jaggi type contractions in this new setting. Our results extend, unify and generalize many existing fixed point theorems in the literature, including those of Banach, Kannan, Reich, Dass-Gupta, and recent results in -metric, extended b-metric, and orthogonal metric spaces. We support our theoretical findings with non-trivial examples and original geometric diagrams that illustrate the convergence behavior of iterative sequences. As applications, we utilize our main results to establish the existence and uniqueness of solutions for nonlinear matrix equations of the form X = Q + A*F (X) A and for a class of nonlinear fractional Volterra integral equations arising in viscoelasticity theory. Numerical simulations are provided to validate the applicability of our theoretical results.