Compacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarieʼs fractional derivative

In this Letter, the fractional variational iteration method using Heʼs polynomials is implemented to construct compacton solutions and solitary pattern solutions of nonlinear time-fractional dispersive KdV-type equations involving Jumarieʼs modified Riemann–Liouville derivative. The method yields solutions in the forms of convergent series with easily calculable terms. The obtained results show that the considered method is quite effective, promising and convenient for solving fractional nonlinear dispersive equations. It is found that the time-fractional parameter significantly changes the soliton amplitude of the solitary waves.

► Some nonlinear time-fractional dispersive KdV-type equations are solved.
► An effective and convenient method is considered.
► Compacton solutions and solitary pattern solutions are obtained.
► The obtained solutions may give insight into many considerable physical processes.