Solution of Nonlinear Space-Time Fractional Differential Equations Using the Fractional Riccati Expansion Method. (22nd December 2013)

• Record Type: Journal Article
• Authors: Abdel-Salam, Emad A.-B.; Yousif, Eltayeb A.
• Other Names: Swierniak Andrzej Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-12-22
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/846283
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.