Bulgarian Academy of Sciences - National Committee for Mathematics
Mathematica Balkanica New Series, Vol. 26, Fasc 1-2 (2012), 35p-48p
The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of the Fox H-functions. The results derived are of general nature and include already known results as particular cases.