University of TabrizComputational Methods for Differential Equations2345-39829420211001Toward a new understanding of cohomological method for fractional partial differential equations9599761214910.22034/cmde.2020.39020.1710ENAkbarDehghan NezhadDepartment of Mathematics,
Iran University of Science and Technology,
P.O.Box, 16846-13114, Narmak, Tehran, Iran.0000-0003-4200-6892MinaMoghaddamDepartment of Mathematics,
Iran University of Science and Technology,
P.O.Box, 16846-13114, Narmak, Tehran, Iran.Journal Article20200327One 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.https://cmde.tabrizu.ac.ir/article_12149_aad783037037f608aca30ca104ac82f0.pdf