This paper presents an accurate numerical method for solving fractional Riccati differential
equation (FRDE). The proposed method so called fractional Chebyshev finite difference
method (FCheb-FDM). In this technique, we approximate FRDE with a finite dimensional problem.
The method is based on the combination of the useful properties of Chebyshev polynomials
approximation and finite difference method. The Caputo fractional derivative is replaced by a difference
quotient and the integral by a finite sum. By this method the given problem is reduced to a
problem for solving a system of algebraic equations, and by solving this system, we obtain the solution
of FRDE. Special attention is given to study the convergence analysis and estimate an error
upper bound of the obtained approximate formula. Illustrative examples are included to demonstrate
the validity and applicability of the proposed technique.