Exact solutions of some systems of fractional differential‐difference equations. (2nd December 2014)

• Record Type: Journal Article
• Authors: Bekir, Ahmet; Güner, Özkan; Ayhan, Burcu
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 3807
• Page End: 3817
• Publication Date: 2014-12-02
• Subjects: fractional differential‐difference equations -- fractional partial differential equations -- exact solutions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3318
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, the G ′ G ‐expansion method is proposed to establish hyperbolic and trigonometric function solutions for fractional differential‐difference equations with the modified Riemann–Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential‐difference equation into its differential‐difference equation of integer order. We obtain the hyperbolic and periodic function solutions of the nonlinear time‐fractional Toda lattice equations and relativistic Toda lattice system. The proposed method is more effective and powerful for obtaining exact solutions for nonlinear fractional differential–difference equations and systems. Copyright © 2014 John Wiley & Sons, Ltd.