Approximate analytical solutions of the nonlinear fractional order financial model by two efficient methods with a comparison study

The financial system has become prominent and important in global economics because the key to stabilizing the economy is to secure or control the financial system or market.
The goal of this study is to determine whether or not the approximate analytical series solutions obtained by the residual power series method and Elzaki transform decomposition method of the fractional nonlinear financial model satisfy economic theory. The fractional derivative is used in the sense of the Caputo derivative.
The results are depicted numerically and in figures that show the behavior of the approximate solutions of the interest rate, investment demand, and price index. Both methods yielded results in accordance with economic theory, which established that researchers could apply these two methods to solve all types of fractional nonlinear problems that arise in financial systems.