Exact solutions of some systems of fractional differential‐difference equations

E-ISSN： 1099-1476|38|17|3807-3817

ISSN： 0170-4214

Source： MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Vol.38, Iss.17, 2015-11, pp. : 3807-3817

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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.