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 - http://dx.doi.org/10.1016/j.physa.2011.12.035
SN - 0378-4371 (print)
SN - 1873-2119 (online)
VL - 391
IS - 8
SP - 2527
EP - 2542
PB - Elsevier
CY - Amsterdam
ER -