Exact fractional soliton solutions of thin-film ferroelectric material equation by analytical approaches

Abstract

In this paper, the main motive is to mathematical explore the thin-film ferroelectric material partial differential equation which addresses the Ferroelectrics, that are being examined as key materials for applications in piezoelectric, pyroelectric electrostrictive, linear, and nonlinear optical systems. Thin ferroelectric films are used in a variety of modern electrical devices because they are both nonlinear ferroelectric and dielectric materials. This article appropriates the fractional travelling wave transformation allowing the partial differential equation to be changed into an ordinary differential equation. The considered fractional model is explored through employing the combo of G′G2−expansion method and new extended direct algebraic methodology. As an outcome, numerous types of soliton solutions like, Periodic pattern with anti-peaked crests and anti-troughs, singular solution, mixed complex solitary shock solution, mixed singular solution, mixed shock singular solution, mixed trigonometric solution, mixed periodic, periodic solution and mixed hyperbolic solution obtain via Mathematica. In addition, the G′G2−expansion technique produces singular, trigonometric, and hyperbolic solutions with different soliton families. The revealed solution will improve the mathematical analysis of this model and the associated physical phenomenon's. In order to visualize the graphical propagation of the obtained fractional soliton solutions, 3D, 2D, and contour graphics are generated by choosing appropriate parametric values. The impact of fractional parameter β is also graphically displayed on the propagation of solitons.