Journal of Applied Mathematics & Bioinformatics

Spectral method for fractional quadratic Riccati differential equation

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• Abstract

  Fractional differentials provide more accurate models of systems under consideration. In this paper, approximation techniques based on the shifted Legendre spectral method is presented to solve fractional Riccati differential equations. The fractional derivatives are described in the Caputo sense. The technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of nonlinear algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use.