Volume 5, Issue 6
A Collocation Method for Solving Fractional Riccati Differential Equation

Mustafa Gülsu, Yalçın Öztürk & Ayşe Anapali

Adv. Appl. Math. Mech., 5 (2013), pp. 872-884.

Published online: 2013-05

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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

Riccati equation fractional derivative collocation method generalized Taylor series approximate solution

  • AMS Subject Headings

34A08 656N35 30K05

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COPYRIGHT: © Global Science Press

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@Article{AAMM-5-872, author = {Mustafa Gülsu, Yalçın Öztürk and Ayşe Anapali}, title = {A Collocation Method for Solving Fractional Riccati Differential Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {6}, pages = {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 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m12118}, url = {http://global-sci.org/intro/article_detail/aamm/101.html} }
TY - JOUR T1 - A Collocation Method for Solving Fractional Riccati Differential Equation AU - Mustafa Gülsu, Yalçın Öztürk & Ayşe Anapali JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 872 EP - 884 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.12-m12118 UR - https://global-sci.org/intro/article_detail/aamm/101.html KW - Riccati equation KW - fractional derivative KW - collocation method KW - generalized Taylor series KW - approximate solution AB -

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.

Mustafa Gülsu, Yalçın Öztürk & Ayşe Anapali. (1970). A Collocation Method for Solving Fractional Riccati Differential Equation. Advances in Applied Mathematics and Mechanics. 5 (6). 872-884. doi:10.4208/aamm.12-m12118
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