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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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