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Toward a new understanding of cohomological method for fractional partial differential equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 دی 1399 اصل مقاله (264.54 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.39020.1710 | ||
| نویسندگان | ||
Akbar Dehghan Nezhad   1؛ Mina Moghaddam2
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| 1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846 -13114, Iran | ||
| 2School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846 -13114, Iran. | ||
| چکیده | ||
| One of the aims of this article is to investigate the solvability and unsolvability conditions for fractional cohomological equation $ \psi^{\alpha} f=g $, on $ \mathbb{T}^n $. We prove that if $ f $ is not analytic, then fractional integro-differential equation $ I_t^{1-\alpha} D_x^{\alpha}u(x,t)+i I_x^{1-\alpha} D_t^{\alpha}u(x,t)=f(t) $ has no solution in $ C^1(B) $ with $0< \alpha \leq 1$. ٌWe also obtain solutions for the space-time fractional heat equations on $ \mathbb{S}^1 $ and $ \mathbb{T}^n $. At the end of this article, there are examples of fractional partial differential equations and a fractional integral equation together with their solutions. | ||
| کلیدواژه‌ها | ||
| Fractional calculus؛ fractional cohomological equations؛ space-time-fractional heat equation؛ solvable and unsolvable fractional differential equations | ||
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آمار تعداد مشاهده مقاله: 6 تعداد دریافت فایل اصل مقاله: 29 |
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