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

One of the aims of this article is to investigate the solvability and unsolvability conditions for fractional cohomological equation f = g, on Tn. We prove that if f is not analytic, then fractional integro-differential equation I1 t D x u(x; t) + iI1 x D t u(x; t) = f(t) has no solution in C1(B) with 0 < 1. We also obtain solutions for the space-time fractional heat equations on S1 and Tn. At the end of this article, there are examples of fractional partial differential equations and a fractional integral equation together with their solutions.