Computational Fractional Dynamical Systems

23Fractional Subequation Method

23.1 Introduction

Based on the results obtained by (Zhang et al. 2010), Zhang and Zhang (2011) recently developed a novel algebraic approach called the fractional subequation method for determining the traveling wave solutions to nonlinear fractional partial differential equations (FPDEs). The homogeneous balancing principle (Wang 1999) and Jumarie's modified Riemann‐Liouville derivative of fractional order (Jumarie 2006) is used in this technique. Zhang et al. Zhang and Zhang 2011) used this technique to derive traveling wave solutions for the nonlinear time fractional biological population model and the (4 + 1)‐dimensional space–time fractional Fokas equation. The traveling wave solutions of the space–time fractional mBBM equation and the ZKBBM equation (Alzaidy 2013a) were obtained using this approach. The space–time fractional Potential Kadomtsev–Petviashvili (PKP) equation and the space–time fractional symmetric regularized long wave (SRLW) equation have both been solved using the subequation approach (Alzaidy 2013b). This approach was utilized by (Yépez‐Martínez et al. 2014) to establish analytical solutions for the space–time fractional coupled Hirota‐Satsuma Korteweg de Vries (KdV) and modified Korteweg de Vries (mKdV) equations. The fractional subequation method employing Jumarie's modified Riemann‐Liouville derivative was used by (Mohyud‐Dina et al. 2017) to produce analytical solutions of the space–time fractional Calogero‐Degasperis ...