TY  - JOUR
T1  - Exact Solutions of Time-Fractional Thin-Film Ferroelectric Material Equation with Conformable Fractional Derivative
TT  - Exact Solutions of Time-Fractional Thin-Film Ferroelectric Material Equation with Conformable Fractional Derivative
AU  - Ekici, Mustafa
PY  - 2025
DA  - January
Y2  - 2024
DO  - 10.34248/bsengineering.1575776
JF  - Black Sea Journal of Engineering and Science
JO  - BSJ Eng. Sci.
PB  - Karyay Karadeniz Yayımcılık Ve Organizasyon Ticaret Limited Şirketi
WT  - DergiPark
SN  - 2619-8991
SP  - 179
EP  - 184
VL  - 8
IS  - 1
LA  - en
AB  - This study employs the unified method, a powerful approach, to address the intricate challenges posed by fractional differential equations in mathematical physics. The principal objective of this study is to derive 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, 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.
KW  - The thin-film ferroelectric material equation
KW  - The unified method
KW  - Conformable fractional derivative
N2  - This study employs the unified method, a powerful approach, to address the intricate challenges posed by fractional differential equations in mathematical physics. The principal objective of this study is to derive 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, 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.
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UR  - https://doi.org/10.34248/bsengineering.1575776
L1  - https://dergipark.org.tr/tr/download/article-file/4324344
ER  -