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Dehghan Nezhad, Akbar, Moghaddam, Mina. (1400). Toward a new understanding of cohomological method for fractional partial differential equations. سامانه مدیریت نشریات علمی, 9(4), 959-976. doi: 10.22034/cmde.2020.39020.1710
Akbar Dehghan Nezhad; Mina Moghaddam. "Toward a new understanding of cohomological method for fractional partial differential equations". سامانه مدیریت نشریات علمی, 9, 4, 1400, 959-976. doi: 10.22034/cmde.2020.39020.1710
Dehghan Nezhad, Akbar, Moghaddam, Mina. (1400). 'Toward a new understanding of cohomological method for fractional partial differential equations', سامانه مدیریت نشریات علمی, 9(4), pp. 959-976. doi: 10.22034/cmde.2020.39020.1710
Dehghan Nezhad, Akbar, Moghaddam, Mina. Toward a new understanding of cohomological method for fractional partial differential equations. سامانه مدیریت نشریات علمی, 1400; 9(4): 959-976. doi: 10.22034/cmde.2020.39020.1710

Toward a new understanding of cohomological method for fractional partial differential equations

Computational Methods for Differential Equations
مقاله 3، دوره 9، شماره 4، دی 2021، صفحه 959-976  XML اصل مقاله (203.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.39020.1710
نویسندگان
Akbar Dehghan Nezhad email orcid ؛ Mina Moghaddam
Department of Mathematics, Iran University of Science and Technology, P.O.Box, 16846-13114, Narmak, Tehran, Iran.
چکیده
One of the aims of this article is to investigate the solvability and unsolvability conditions for fractional cohomological equation ψ αf = g, on T n. We prove that if f is not analytic, then fractional integro-differential equation I 1−α t Dα x u(x, t) + iI1−α x Dα t u(x, t) = f(t) has no solution in C1 (B) with 0 < α ≤ 1. We also obtain solutions for the space-time fractional heat equations on S 1 and 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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