The extended Power Series (XPS) method can be extremely useful for solving nonlinear equations with regular and irregular singular points. The extended power series is considered times a logarithm or times a fractional power of xi, etc.). This research shows it is simple to solve approximately the Perkins-Kern-Nordgren (PKN) model of hydraulic fracture. To illustrate the effectiveness and convenience of the XPS method, we consider the two cases of dimensionless PKN equation containing the M-scaling and M ̃-scaling. The results compared with available analytical results verified excellent agreements.
