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International Journal of Differential Equations
Volume 2012 (2012), Article ID 346089, 17 pages
http://dx.doi.org/10.1155/2012/346089
Research Article

On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative

Department of Mathematics Engineering, Gümüşhane University, 29100 Gümüşhane, Turkey

Received 10 December 2011; Accepted 6 March 2012

Academic Editor: Ebrahim Momoniat

Copyright © 2012 Mehmet Merdan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. The behavior of the solutions and the effects of different values of fractional order 𝛼 are indicated graphically. The results obtained by the FVIM reveal that the method is very reliable, convenient, and effective method for nonlinear differential equations with modified Riemann-Liouville derivative