Application of extended Fan sub-equation method to $(1+1)$-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution

The article studies the application of the extended Fan sub-equation method to $(1+1)$-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution. This equation describes the hydromagnetic waves in cold plasma, acoustic waves in inharmonic crystals and acoustic gravity waves in compressible fluids. The structure of the extended Fan sub-equation method on the basis of time-fractional derivative is presented. The main idea of the method is to take full advantage of the general elliptic equation involving five parameters. The fractional derivatives are taken as in the sense of Jumarie's modified Riemann–Liouville derivative. The method is reliable and gives more general exact solutions than the existing methods.