Partial Differential Equations in Applied Mathematics (Dec 2023)
An analytical technique to obtain traveling wave solutions to nonlinear models of fractional order
Abstract
The (3, 3, 3) time-fractional Zakharov–Kuznetsov (TFZK) equation demonstrates the characteristic of traffic flows, the viscoelasticity waves, the material science, sound waves, signal processing, the financial mathematics, optical fibers, the electromagnetic field, water wave mechanics, ion acoustic waves in plasmas, the chemical physics and so many. The (3, 3, 3) TFZK equation is the specific event of the general (a,b,c) TFZK equation, where a,b denote the space coordinates and c denotes the temporal coordinate. The object of this investigation is to consider determining the (3, 3, 3) TFZK equation by the modified (G′/G)-expansion scheme (MGD/GES). The derivatives are in the beta-derivative sense. The fractional transformation equation is utilized to convert the proposed nonlinear models of fractional order (NLMFO) into non-linear models of integer order. Additionally, numerous new wave solutions (WSs) are formed. The attractive and easy technique of the MGD/GES recommends that this technique can be applied to WSs of other NLMFOs straightforwardly.
