An improved analytical approach to establish the soliton solutions to the time‐fractional nonlinear evolution models

Abstract

The time‐fractional Schrödinger (higher dimensional) and the Zakharov–Kuznetsov (ZK) models are the noteworthy modeling equations to interpret the propagation of signal in nonlinear optical fibers, small‐amplitude gravity waves on the surface water, high frequency acoustic waves, the interactions of small amplitude waves, the ion acoustic waves, nonlinear optics, Bose‐Einstein condensates, dynamics of plasma particles, etc. In this article, in order to develop advanced and broad‐spectrum closed‐form soliton solutions of the previously described nonlinear models, the advanced auxiliary equation approach has been put in used with reference to the beta‐derivative concept. The established soliton solutions are further comprehensive and typical and found in the form fractional, exponential, hyperbolic, and trigonometric functions and their variation. We depict 3D shape of the obtained solitons and explain the physical significance of the solitons. The accomplished solutions affirm that the method is effective and powerful and yields compatible solutions to fractional nonlinear evolution equations.