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 known DξαG(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.