## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2013 (2013), Article ID 598083, 8 pages.

### A Collocation Method for Solving Fractional Riccati Differential Equation

Yalçın Öztürk, Ayşe Anapalı, Mustafa Gülsu, and Mehmet Sezer

#### Abstract

We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. 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, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.

#### Article information

**Source**

J. Appl. Math., Volume 2013 (2013), Article ID 598083, 8 pages.

**Dates**

First available in Project Euclid: 14 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1394808096

**Digital Object Identifier**

doi:10.1155/2013/598083

**Mathematical Reviews number (MathSciNet)**

MR3092006

**Zentralblatt MATH identifier**

1305.34014

#### Citation

Öztürk, Yalçın; Anapalı, Ayşe; Gülsu, Mustafa; Sezer, Mehmet. A Collocation Method for Solving Fractional Riccati Differential Equation. J. Appl. Math. 2013 (2013), Article ID 598083, 8 pages. doi:10.1155/2013/598083. https://projecteuclid.org/euclid.jam/1394808096