This work suggests a new analytical technique called the fractional homotopy perturbation method (FHPM) for solving fractional differential equations of any fractional order. This method is based on He's homotopy perturbation method and the modified Riemann-Liouville derivative. The fractional differential equations are described in Jumarie's sense. The results from introducing a modified Riemann-Liouville derivative in the cases studied show the high accuracy, simplicity and efficiency of the approach. (C) 2011 Elsevier Ltd. All tights reserved.