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Numerical Approaches to the Time-Fractional Burgers' Equation Using the Conformable Fractional Derivative | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 09 آبان 1404 اصل مقاله (2.24 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65450.3011 | ||
| نویسنده | ||
| Bilge Inan* | ||
| Department of Engineering Sciences, Iskenderun Technical University, Hatay, 31200, Turkiye. | ||
| چکیده | ||
| In the present study, we develop two exponential finite difference methods that are effectively applied to obtain numerical solutions of the time-fractional nonlinear Burgers' equation involving a conformable derivative. To evaluate the effectiveness of the proposed methods, three test problems are considered, with the fractional order parameter $\alpha $ chosen in the range $0<\alpha \leq 1$. Furthermore, to verify the reliability of the methods, we set $\alpha = 1$ to recover the classical first-order derivative and compare the resulting approximate solutions with the corresponding exact solutions. The numerical results demonstrate that the proposed methods are both efficient and easy to implement for solving time-fractional Burgers-type differential equations. | ||
| کلیدواژه‌ها | ||
| Time-fractional Burgers' equation؛ Exponential finite difference method؛ Conformable fractional derivative | ||
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آمار تعداد مشاهده مقاله: 126 تعداد دریافت فایل اصل مقاله: 299 |
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