In this paper, we present a novel approach for speech signal modeling using fractional calculus. This approach is contrasted with the celebrated Linear Predictive Coding (LPC) approach which is based on integer order models. It is demonstrated via numerical simulations that by using a few integrals of fractional orders as basis functions, the speech signal can be modeled accurately. The new approach has the merit of requiring a smaller number of model parameters, and is demonstrated to be superior to the LPC approach in capturing the details of the modeled signal. ©2007 IEEE.