Atomic solutions of some fractional partial differential equations

We offer a comprehensive example to showcase the atomic solution method for finding all possible atomic solutions to specific fractional partial differential equations, which are often difficult to solve with traditional methods like separation of variables. This approach is based on principles from tensor product theory in Banach spaces and the properties of atomic operators. By representing the solution as a tensor product of two functions, the method allows for a more efficient and structured way of solving these equations. This example highlights how the atomic solution method can overcome the limitations of conventional techniques, providing a clearer pathway to identifying solutions that may be otherwise elusive. Through this approach, we demonstrate the potential of atomic operators and tensor product theory to simplify the resolution of complex fractional partial differential equations, broadening the range of solvable problems in this field. Mathematics Subject Classification (2010). 35E99, 47B01.