This work focuses on the development and analysis of a financial system using advanced mathematical modeling techniques. Starting from an ordinary financial system, we extend it to a fractional-order framework by incorporating the Caputo fractional-order operator. The fractional differential equations are solved both analytically and numerically. Analytical solutions are derived using the Elzaki transform method, providing deeper insights into the system’s dynamics. Stability analysis is performed to identify equilibrium points and derive precise conditions for system stability. Furthermore, we explore chaotic behavior within the system and propose effective control strategies using the feedback control method to regulate its dynamics. The results offer significant contributions to understanding and managing complex financial systems, enabling improved decision-making in financial analysis and policy design.
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