TY - JOUR A1 - Tomovski, Zivorad A1 - Sandev, Trifce A1 - Metzler, Ralf A1 - Dubbeldam, Johan T1 - Generalized space-time fractional diffusion equation with composite fractional time derivative JF - Physica : europhysics journal ; A, Statistical mechanics and its applications N2 - We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0). KW - Fractional diffusion equation KW - Composite fractional derivative KW - Riesz-Feller fractional derivative KW - Mittag-Leffler functions KW - Fox H-function KW - Fractional moments KW - Asymptotic expansions KW - Grunwald-Letnikov approximation Y1 - 2012 U6 - https://doi.org/10.1016/j.physa.2011.12.035 SN - 0378-4371 SN - 1873-2119 VL - 391 IS - 8 SP - 2527 EP - 2542 PB - Elsevier CY - Amsterdam ER -