Generalized θ-parametric metric spaces: fixed point theorems and application to fractional economic growth model via fractional differential approach

The objective of this manuscript is to introduce and develop the concept of a generalized θ-parametric metric space, a novel extension that enriches the modern metric fixed point theory. We study its fundamental properties, including convergence and Cauchy sequences, which establishes a solid theoretical foundation. A significant highlight of our work is the formulation of the Suzuki-type fixed point theorem within this framework, which extends classical results in a meaningful way. To demonstrate the depth and applicability of our findings, we construct non-trivial examples that illustrate the behavior of key concepts. Moreover, as a practical application, we apply our main theorem to analyze an economic growth model, demonstrating its utility in solving fractional differential equations that arise in dynamic economic systems.