The fundamental solution of a diffusion-wave equation of fractional order. (English) Zbl 1172.26001

Pskhu, A. V.

Izv. Math. 73, No. 2, 351-392 (2009); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 73, No. 2, 141-182 (2009).

The author constructs a solution of a very general time fractional diffusion-wave equation with the Dzhrbashyan-Nersesyan fractional derivative in a very large paper, which is written with great rigor. Such results are generalizations of the corresponding well-known ones for the Riemann-Liouville and Caputo fractional derivatives. We have to remark that in the large list of references the author forgot to include one of the last books on fractional differential equations published during the last years.

Reviewer: Juan J. Trujillo (La Laguna)

MSC:

26A33	Fractional derivatives and integrals
35A08	Fundamental solutions to PDEs
35S10	Initial value problems for PDEs with pseudodifferential operators

Keywords:

Dzhrbashyan-Nersesyan fractional derivative; time-fractional diffusion-wave equation; fundamental solution