(7) An analytical method for space–time fractional nonlinear differential equations arising in plasma physics
Mohamed Aly Abdou
Physics Department, College of Science and Home Domestics, University of Bisha, Bisha, Saudi Arabia
Received 21 February 2017; received in revised form 27 July 2017; accepted 8 September 2017
Available online 18 September 2017
Abstract
Here, a new fractional sub-equation method with a fractional complex transform is proposed for constructing exact solutions of fractional partial differential equations arising in plasma physics in the sense of modified Riemann–Liouville derivative, which is the fractional version of the knownD αξ G (ξ )/G (ξ ) method. To illustrate the validity of this method, we apply it to the space–time fractional KdV equation on the dust ion acoustic waves in dusty plasma and space–time Boussinesq fractional equation. The proposed approach is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations. The solutions obtained here are new and have not been reported in former literature.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Keywords: New frcational subequation method; Fractional complex transformation; Riemann–Liouville derivative; Exact solutions.