Compact structures in a class of nonlinearly dispersive equations with time-fractional derivatives

In this work, variants of the KdV equation with time-fractional derivatives, which exhibits compactons: solitons with compact support, are investigated. New solitary-wave solutions with compact support are developed. The homotopy perturbation method is employed to derive compact solutions for these variants. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. The proposed scheme can be used to construct compact and noncompact solutions for a wide class of nonlinear fractional evolution equations.