Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations

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Communications in Theoretical Physics ›› 2016, Vol. 65 ›› Issue (02): 177-184.

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Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations

Qing Huang, Li-Zhen Wang, Su-Li Zuo

School of Mathematics, Northwest University, Xi'an 710069, China;
Center for Nonlinear Studies, Northwest University, Xi'an 710069, China

Received: 2015-10-09 Revised: 2015-12-02 Published: 2016-02-01
Contact: Qing Huang E-mail:hqing@nwu.edu.cn
Funding Information:
Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037

Abstract

Abstract: In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed.

Key words: consistent Riccati expansion, fractional partial differential equation, Riccati equation, modified Riemann-Liouville fractional derivative, exact solution

PACS numbers:

04.20.Jb

Qing Huang, Li-Zhen Wang, Su-Li Zuo, Commun. Theor. Phys. 65 (2016) 177.

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Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations

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