Exact Solutions of Time-Fractional Thin-Film Ferroelectric Material Equation with Conformable Fractional Derivative

Abstract

This study leverages the powerful unified method to address the complex challenges presented by fractional differential equations in mathematical physics. Our primary focus is on deriving novel exact solutions for the time-fractional thin-film ferroelectric material equation. Fractional derivatives in this study are defined using the conformable fractional derivative, ensuring a robust mathematical foundation. Through the unified method, we derive solitary wave solutions for the governing equation, which models wave dynamics in these materials and holds significance in various fields of physics and hydrodynamics. The behavior of these solutions is analyzed using the conformable derivative, shedding light on their dynamic properties. Analytical solutions, formulated in hyperbolic, periodic, and trigonometric forms, reveal dark, bright, periodic, and solitary wave solitons, illustrating the impact of fractional derivatives on these physical phenomena. This paper highlights the capability of the unified method in tackling complex issues associated with fractional differential equations, expanding both mathematical techniques and our understanding of nonlinear physical phenomena.