Abstract
Solitonic solutions have become a popular topic among traveling wave solutions since they act as a bridge between mathematics and physics. In this article, two newly developed methods, namely the extended rational sine-cosine method and extended rational sinh-cosh method by means of fractional complex transform are applied to construct the exact solutions in the form of hyperbolic, trigonometric and rational functions of the nonlinear fractional Phi-4 equation. The obtained solutions are further expressed by solitons, dark solitons, periodic and kink wave solutions. The proposed methods analyze the possibility of the existence of limit cycles with specific parameters.
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