Investigation of Chaotic Finance with Renewable Energy Effects Using Sustainable Fractional Approach - Alhefthi, Reem K.; Ahmad, Aqeel; Abbas, Safdar; İnç, Mustafa; Ghaffar, Abdul; Mustafa, Ghulam (Springer, 2025)
To analyze the financial dynamics of a community, rigorous mathematical modeling is indispensable. This study investigates the XYZ chaotic financial system while accounting for the influence of renewable energy. We propose a mathematical framework that integrates the effects of renewable energy sources into a chaotic financial model with investment demand. To convert the established system into a fractional-order framework, the definition of the Fractal-Fractional Operator (FFO) is employed. A comprehensive numerical and qualitative analysis of the newly developed XYZR system is conducted. The boundedness and uniqueness of the system are investigated to ensure well-defined and reliable outcomes-properties that are crucial for studying chaotic dynamics. Furthermore, the influence of renewable energy sources and the rates of transition within each sub-compartment are analyzed under the Lipschitz condition. The global derivative is shown to preserve positivity and exhibit linear growth behavior. To generate answers for precise approximations, sophisticated operators are employed. To learn more about how chaotic finance actually behaves under renewable energy, simulations are run to examine the effects of renewable energy sources on the chaotic financial system with global minimum interest rate regulations. These studies are useful for measuring the effects of renewable energy based on our supported findings and for comprehending the chaotic behaviour of the financial system.
Keywords: Boundedness; Lipschitz conditions; Mathematical Modeling; Global derivative; Renewable energy effects