New function of Mittag–Leffler type and its application in the fractional diffusion-wave equation

The classical Mittag–Leffler (M–L) functions have already proved their efficiency as solutions of fractional-order differential and integral equations. In this paper we introduce a modified M–L type function and deduce its important integral transforms. Then the solution of the initial-boundary value problem for the so-called fractional diffusion-wave equation with real-order time and space derivatives is given by using the inverse Fourier transform of the new function.