Soliton solutions for the space-time nonlinear partial differential equations with fractional-orders

Many practical models in interdisciplinary fields can be described with the help of fractional-order nonlinear partial differential equations(NPDEs). Fractional-order NPDEs such as the space-time fractional Fokas equation, the space-time Kaup–Kupershmidt equation and the space-time fractional (2+1)-dimensional breaking soliton equation have been widely applied in many branches of science and engineering. So, finding exact traveling wave solutions are very helpful in the theories and numerical studies of such equations. More precisely, fractional sub-equation method together with the proposed technique is implemented to obtain exact traveling wave solutions of such physical models involving Jumarie’s modified Riemann–Liouville derivative. As a result, some new exact traveling wave solutions for them are successfully established. Also, (1+1)-dimensional plots and 1-dimensional plots of some of the derived solutions are given to visualize the dynamics of the considered NPDEs. The obtained results reveal that the proposed technique is quite effective and convenient for obtaining exact solutions of NPDEs with fractional-order.