A Collocation Method for Solving Fractional Riccati Differential Equation

A Collocation Method for Solving Fractional Riccati Differential Equation

Year:    2013

Author:    Mustafa Gülsu, Yalçın Öztürk, Ayşe Anapali

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 6 : pp. 872–884

Abstract

In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation. The fractional derivatives are described in the Caputo sense. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, the systems of nonlinear algebraic equation are derived. We further solve the system of nonlinear algebraic equation using Maple 13 and thus obtain the coefficients of the generalized Taylor expansion. Illustrative examples are presented to demonstrate the effectiveness of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-m12118

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 6 : pp. 872–884

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Riccati equation fractional derivative collocation method generalized Taylor series approximate solution.

Author Details

Mustafa Gülsu

Yalçın Öztürk

Ayşe Anapali

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