A numerical study on fractional order financial system with chaotic and Lyapunov stability analysis

In the last few decades, academic research has focused more on financial problems and poverty levels. These are among the two major challenges of the modern world today. To understand the challenge of financial crisis and poverty in societies. This paper explains a deterministic financial system of non linear differential equations. Which aim to provide recommendations to address the twin challenges. In this fractional chaotic model, memory and chaos are portrayed as effects on a system. Financial systems of fractional order have three compartments: interest rate x(t), investment demand rate y(t) and price indexes rate z(t). For the first time, the Legendre wavelet approximation is applied to fractional order financial systems. A major objective of this process is to convert fractional differential equations (FDEs) into algebraic equations by using Legendre wavelets and their fractional integral operators. For residual analysis, convergence and stability analysis, we have used iteration methods and Legendre wavelets. This study indicates good results between the approximate and numerical solutions and that this method is efficient and accurate. Using the iteration method, we prove that the solution exists, while the contraction theory proves its uniqueness. The findings of this study will be extremely useful for future financial management. We have demonstrated the applicability and effectiveness of these methods by analysing numerical simulations for the fractional order financial model and the numerical simulation has been calculated by MATLAB programming.