The Modified Fractional Sub-equation Method and Its Applications to Nonlinear Fractional Partial Differential Equations

It is well known that fractional differential equations appeared more and more frequently in different research areas, such as fluid mechanics, viscoelasticity, biology, physics, engineering and other areas of science [1-30]. Considerable attention have been spent in recent years to develop techniques to look for solutions of nonlinear fractional partial differential equations (NFPDEs). Consequently, a lot of powerful methods for solving fractional differential equations were proposed, such as Adomian decomposition method [11], differential transform method [12], variational iteration method [13], homotopy perturbation method [14, 26-29], the exp-function method [15, 16] and so on. Most recently, according to homogeneous balance principle and Jumarie’s modified Riemann-Liouville derivative, Zhang and Zhang [17] presented a novel technique, that is fractional sub-equation method, to look for exact solutions to nonlinear time fractional biological population model and (4+1)dimensional space-time fractional Fokas equation. Then, Guo et al. [18] modified this method and obtained the exact solutions of the space-time fractional WhithamBroer-Kaup and generalized Hirota-Satsuma coupled KdV equations. In [19], the authors get the exact solutions of NFPDEs by using of Bäcklund transformation of fractional Riccati equation method.