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A Collocation Method for Solving Fractional Riccati Differential Equation

Published online by Cambridge University Press:  03 June 2015

Mustafa Gülsu ,
Yalçın Öztürk  and
Ayşe Anapali
Mustafa Gülsu
Affiliation:
Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Mugla, Turkey
Yalçın Öztürk*
Affiliation:
Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Mugla, Turkey
Ayşe Anapali
Affiliation:
Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Mugla, Turkey
*
*Corresponding author. Email: [email protected]
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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 is 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.

Keywords

34A08656N330K05Riccati equationfractional derivativecollocation methodgeneralized Taylor seriesapproximate solution
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 6 , December 2013 , pp. 872 - 884
Copyright
Copyright © Global-Science Press 2013

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