The fundamental solutions for the fractional diffusion-wave equation Original Research Article

The time fractional diffusion-wave equation is obtained from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative of order 2β with View the MathML source or View the MathML source, respectively. Using the method of the Laplace transform, it is shown that the fundamental solutions of the basic Cauchy and Signalling problems can be expressed in terms of an auxiliary function M(z;β), where View the MathML source is the similarity variable. Such function is proved to be an entire function of Wright type.