Abuandant fractional soliton solutions of a space-time fractional perturbed Gerdjikov-Ivanov equation by a fractional mapping method

Abstract A new fractional mapping method based on a generalized fractional auxiliary equation is proposed and applied to solve the space-time fractional perturbed Gerdjikov-Ivanov equation. The main feature of this approach is to obtain more accurate solutions by means of an auxiliary equation. Some exact fractional nonlinear wave solutions, including bright soliton, periodical wave and singularity soliton solutions are constructed by Mittag–Leffler function. Some deformations appear in those fractional nonlinear wave solutions, and those deformations become more obvious with the increase of the fractional order parameter. In addition, the coefficient of group velocity dispersion and the self-steepening for short pulses also affect the intensity of the soliton when the fractional order parameter remains unchanged. The effect of fractional order is explained by the graphical representation of a series of solutions and their physical meanings.