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Fractional Chebyshev differential equation on symmetric $\alpha$ dependent interval | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 مرداد 1402 اصل مقاله (1.08 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2023.54630.2275 | ||
| نویسندگان | ||
| Zahra Kavooci1؛ Kazem Ghanbari* 1، 2؛ Hanif Mirzaei1 | ||
| 1Faculty of Sciences, Sahand University of Technology, Tabriz, Iran. | ||
| 2School of Mathematics and Statistics, Carleton University, Ottawa, Canada. | ||
| چکیده | ||
| Most of fractional differntial equations are considered on a fixed interval. In this paper we consider a typical fractional differential equation on a symmetric interval $[-\alpha,\alpha]$, where $\alpha$ is the order of fractional derivative. For a positive real number $\alpha$ we prove that the solutions are $T_{n,\alpha}(x)=(\alpha+x)^\frac{1}{2}Q_{n,\alpha}(x)$, where $Q_{n,\alpha}(x)$ produce a family of orthogonal polynomials with respect to weight function $w_\alpha(x)=(\frac{\alpha+x}{\alpha-x})^{\frac{1}{2}}$ on $[-\alpha,\alpha]$. For integer case $\alpha=1$ we show that these polynomials coincide with classical Chebyshev polynomials of third kind. Orthogonal properties of the solutions leads to practical results in determining solutions of some fractional differential equations. | ||
| کلیدواژه‌ها | ||
| Orthogonal Polynomials؛ Fractional Chebyshev differential equation؛ Riemann-Liouville and Caputo derivatives | ||
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آمار تعداد مشاهده مقاله: 32 تعداد دریافت فایل اصل مقاله: 44 |
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