Mathematical analysis of the dynamics of solitary wave solutions to the time-fractional thin-film ferroelectric materials model

The thin-film ferroelectric materials equation is a fundamental mathematical model to explain the behavior of polarized electric fields in ferroelectric materials possessing unique properties such as piezoelectricity, pyroelectricity, electrostriction, hysteresis, spontaneous polarization, etc. These significant properties of ferroelectric materials are important in the progress of capacitors, non-volatile memories, electrical sensors, as well as optical and biomedical devices, among other applications. The aim of the present study is to explore applicable soliton solutions to the fractional-order model to the aforementioned equation by addressing the improved F-expansion method. Through analysis and rigorous identification, various radical solutions, including trigonometric, hyperbolic, and rational forms of the model, are established, and significant solitons are restored by setting appropriate parameter values in the analytical solutions obtained, which are demonstrated through 3D, 2D, and contour plots. We also explore the impact of fractional derivative as well as the parameters, like pressure, temperature, and others included in the model to determine the polarization effect in ferroelectric materials. This study uncovers several novel solutions along with their states in response to external or internal field parameters, which might be helpful in understanding the nature of ferroelectric materials.