Haar wavelet method for solving fractional partial differential equations numerically

In this paper, a wavelet operational method based on Haar wavelet is proposed to solve the fractional partial differential equations in the Caputo derivative sense. We give the Haar wavelet operational matrix of fractional order integration. A truncated Haar wavelet series together with the wavelet operational matrix are utilized to reduce the fractional partial differential equations to Sylvester equations. In addition, some examples are presented to show the efficiency and the accuracy of the approach.