TY - JOUR ID - 12149 TI - Toward a new understanding of cohomological method for fractional partial differential equations JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Dehghan Nezhad, Akbar AU - Moghaddam, Mina AD - Department of Mathematics, Iran University of Science and Technology, P.O.Box, 16846-13114, Narmak, Tehran, Iran. Y1 - 2021 PY - 2021 VL - 9 IS - 4 SP - 959 EP - 976 KW - . Fractional calculus KW - Fractional cohomological equations KW - Space-time-fractional heat equation KW - Solvable and unsolvable fractional differential equations DO - 10.22034/cmde.2020.39020.1710 N2 - 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. UR - https://cmde.tabrizu.ac.ir/article_12149.html L1 - https://cmde.tabrizu.ac.ir/article_12149_aad783037037f608aca30ca104ac82f0.pdf ER -