Analytical solitary wave solutions of a time-fractional thin-film ferroelectric material equation involving beta-derivative using modified auxiliary equation method
Xiaoming Wang, Haiqa Ehsan, Muhammad Abbas, Ghazala Akram, Maasoomah Sadaf, Thabet Abdeljawad
Abstract
The main objective of current paper is to examine the impacts of fractional parameters on the dynamic response of soliton waves in a nonlinear time-fractional thin-film ferroelectric materials equation (TFFEME). To achieve such a goal, the TFFEME is first rehabilitated into ordinary differential equation using a complex wave transformation. Solitary wave solutions of the governing equation, representing the dynamics of waves in the material and plays a vital rule in many branches of physics and hydrodynamics, are then constructed through applying the modified auxiliary equation method (MAEM). The extracted solutions are demonstrated using definition of the beta derivative to understand their dynamical behavior. The hyperbolic, periodic and trigonometric function solutions are used to derive the analytical solutions for the given model. As a result, dark, bright, periodic and solitary wave solitons are obtained. The fractional impact of the above derivative on the physical phenomena is observed. The 2D and 3D graphs are also shown to confirm the behavior of analytical wave solutions. • An efficient MAEM is utilized for the solving time-fractional thin-film ferroelectric material equation. • The bright, dark, and periodic traveling wave patterns are produced by choosing the parameters. • The 3D, 2D, and contour plots are shown to help with comprehension of the answers that were found. • The scheme is novel and as far as we are aware, it has never been employed for this purpose before.