Fixed Point Theorems: Exploring Applications in Fractional Differential Equations for Economic Growth

Abstract

The aim of this research is to introduce two new notions, Θ-(Ξ,h)-contraction and rational (α,η)-ψ-interpolative contraction, in the setting of F-metric space and to establish corresponding fixed point theorems. To reinforce understanding and highlight the novelty of our findings, we provide a non-trivial example that not only supports the obtained results but also illuminates the established theory. Finally, we apply our main result to discuss the existence and uniqueness of solutions for a fractional differential equation describing an economic growth model.

Keywords

• fixed point
• F -metric space%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"> <mml:math id="mm67457435"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="fraktur">F</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>-metric space
• Θ-(Ξ,h)-contraction
• fractional differential equations
• economic growth