Based on the theory of fractional differential equations, this paper proposes a simple recursive, iterative scheme for power flow calculation in pure radial networks. The paper determines the network hierarchy formed by the ADT stack through breadth theory. This helps us define the branch sequence of the forward and backward generation in the power flow calculation of the smart distribution network. We ensure that the Jacobian matrix remains unchanged in the smart distribution grid power flow calculation. The interval model is more practical and computationally simpler than the point model. The research results show that the power flow calculation method is efficient based on the fractional differential equation.