%0 Journal Article
%T Toward a new understanding of cohomological method for fractional partial differential equations
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Dehghan Nezhad, Akbar
%A Moghaddam, Mina
%D 2021
%\ 10/01/2021
%V 9
%N 4
%P 959-976
%! Toward a new understanding of cohomological method for fractional partial differential equations
%K . Fractional calculus
%K Fractional cohomological equations
%K Space-time-fractional heat equation
%K Solvable and unsolvable fractional differential equations
%R 10.22034/cmde.2020.39020.1710
%X 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.
%U https://cmde.tabrizu.ac.ir/article_12149_aad783037037f608aca30ca104ac82f0.pdf