Zheng, Bin (\(G'/G\))-expansion method for solving fractional partial differential equations in the theory of mathematical physics. (English) Zbl 1264.35273 Commun. Theor. Phys. 58, No. 5, 623-630 (2012). Summary: In this paper, the (\(G'/G\))-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established. Cited in 85 Documents MSC: 35R11 Fractional partial differential equations 35Q53 KdV equations (Korteweg-de Vries equations) 44A05 General integral transforms Keywords:(\(G'/G\))-expansion method; fractional partial differential equations; exact solutions; fractional complex transformation PDFBibTeX XMLCite \textit{B. Zheng}, Commun. Theor. Phys. 58, No. 5, 623--630 (2012; Zbl 1264.35273) Full Text: DOI