Solving fractional Riccati differential equation based on operational matrices

Abstract

In this paper, the solution of fractional Riccati differential equation by using the operational matrix of shifted Legendre polynomial is discussed. The properties of shifted Legendre polynomials together with the Caputo fractional derivative are used to reduce the problem to the solution of nonlinear algebraic equations. Also the theoretical analysis of shifted Legendre polynomial method such as convergence and error analysis has been discussed. The illustrative examples demonstrate its applicability, validity and simplicity of the approximation scheme.