Atomic exact solution for some fractional partial differential equations in Banach spaces

The use of classical methods to solve some fractional partial differential equations, usually, leads to dead ends with no possible solutions as the separation of variables. Hence, in this paper, we use the theory of tensor product of Banach spaces to find certain exact solutions, called atomic solutions which will give us more than one solution to the proposed problems. As an application, we will find the all possible solutions for some fractional partial differential Burger's type equations and see the behavior of these solutions.