NEW FRACTAL SOLITON SOLUTIONS FOR THE COUPLED FRACTIONAL KLEIN–GORDON EQUATION WITH β-FRACTIONAL DERIVATIVE

Abstract

In this paper, we derive some novel fractal soliton solutions of the coupled fractional Klein–Gordon equation with the [Formula: see text]-fractional derivative via two efficient methods, which are fractal functional variable method and fractal sech-function method. The two new mathematical schemes are quite concise and effective, and then numerous new exact fractal soliton solutions of other nonlinear fractal evolution equations can be obtained. Finally, some 3D figures are sketched to describe these new fractal soliton solutions.