Huang, Fenghui; Liu, Fawang The time fractional diffusion and wave equations in an \(n\)-dimensional half space with mixed boundary conditions. (English) Zbl 1362.35321 Pac. J. Appl. Math. 1, No. 4, 409-419 (2009). Summary: In this paper, we consider the time fractional diffusion and wave equations (TFD-WEs) in an \(n\)-dimensional half-space with mixed boundary conditions. W. R. Schneider and W. Wyss [J. Math. Phys. 30, No. 1, 134–144 (1989; Zbl 0692.45004)] derived the solutions in terms of the Green functions but failed to provide the expressions of the Green functions except for some very special cases. This is one of the main purposes of this work to derive the expressions of the Green functions for the TFDWEs in an \(n\)-dimensional half-space with mixed boundary conditions. We will show that the Green functions are non-negative for all cases and can be expressed by the special functions. MSC: 35R11 Fractional partial differential equations 35K05 Heat equation 35L05 Wave equation 35J08 Green’s functions for elliptic equations Keywords:Caputo fractional derivative; Green function; Laplace and Mellin transforms Citations:Zbl 0692.45004 PDFBibTeX XMLCite \textit{F. Huang} and \textit{F. Liu}, Pac. J. Appl. Math. 1, No. 4, 409--419 (2009; Zbl 1362.35321)