Abstract
In the present study, a collocation approach based on various polynomial basis functions for solving the nonlinear Riccati differential equation of fractional-order is presented. Indeed, to obtain approximate solutions the fractional-order Bessel, Chelyshkov, and Legendre functions are used. Using the collocation points, representing the solution and its fractional derivative (in the Caputo sense) in matrix forms, and the matrix operations, the proposed technique converts a solution of the initial-value problem for the Riccati equation into a system of algebraic equations. The efficiency and superiority of the presented method are examined through some test problems and a comparison has been made with well-established computational techniques as well as the analytical exact solutions. It is shown that the proposed method with fractional functions can provide the solution to the equation with better accuracy than its non-fractional counterparts.

Mohammad Izadi. (2019) Fractional polynomial approximations to the solution of fractional Riccati equation, Punjab University Journal of Mathematics, Volume 51, Issue 11.
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