SEMI-ANALYTICAL ITERATIVE METHODS FOR SOLVING TIME-FRACTIONAL RICCATI DIFFERENTIAL EQUATION

Abstract

In this paper, two semi-analytical methods for solving the time-fractional Riccati differential equation, the homotopy perturbation method (HPM) and the modified new iterative method (MNIM), are employed to solve the time-fractional Riccati equation, which is characterized by its nonlinear and fractional-order nature, and serves as a fundamental model in 
mathematical physics and engineering processes involving memory and hereditary properties. By incorporating the Caputo fractional derivative, the study captures the nonlocal temporal dynamics of the system. The MNIM is formulated to enhance convergence and minimize computational complexity, while HPM is utilized to construct an approximate analytical series solution without linearization or discretization. Both methods yield rapidly convergent series solutions that approximate the exact analytical solution with high accuracy. We considered two test cases, and 
the results demonstrated the efficiency, simplicity, and robustness of the proposed methods for various fractional orders, establishing both methods as powerful tools for fractional nonlinear differential equations in applied sciences and engineering. The paper lies in applying semi
analytical iterative methods tailored to the time-fractional Riccati differential equation, providing accurate approximate solutions with reduced computational complexity.