A Collocation Method for Solving Fractional Riccati Differential Equation (Advances in Applied Mathematics and Mechanics, 2021)
In this article, we have introduced a Taylor collocation method,which is based on collocation method for solving fractional Riccatidifferential equation. The fractional derivatives are described inthe Caputo sense. This method is based on first taking the truncatedTaylor expansions of the solution function in the fractional Riccatidifferential equation and then substituting their matrix forms intothe equation. Using collocation points, the systems of nonlinearalgebraic equation are derived. We further solve the system ofnonlinear algebraic equation using Maple 13 and thus obtain thecoefficients of the generalized Taylor expansion. Illustrativeexamples are presented to demonstrate the effectiveness of theproposed method.