This thesis addresses the formulation, modification, and analysis of a fractional-order financial model describing the dynamic relationships among four key economic variables: the interest rate , price index , investment demand , and saving amount . The model is initially expressed as a system of four fractional-order differential equations and solved approximately using the Sumudu–Adomian Decomposition Method (SADM).

Beyond the initial formulation, two modified versions of the system are proposed to better incorporate practical economic constraints and enhance model realism. For each version, rigorous mathematical analysis is conducted to establish the non-negativity and boundedness of solutions, ensuring economic interpretability of the variables over time. The equilibrium points of both the original and modified systems are determined analytically, and their stability properties are examined through linearization techniques and symbolic computation using Wolfram Mathematica.

Approximate analytical solutions are obtained via SADM for all cases, enabling qualitative assessment of the system’s dynamic behavior. This work not only demonstrates the applicability of fractional calculus in modeling complex financial interactions with memory effects but also provides methodological insights for stability and bifurcation analysis of nonlinear fractional systems. The findings contribute to the broader understanding of fractional-order economic modeling and offer a foundation for further research in stability theory, numerical approximation, and the impact of variable-order derivatives on financial dynamics.