35967
2012
2012
eng
2527
2542
16
8
391
article
Elsevier
Amsterdam
1
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Generalized space-time fractional diffusion equation with composite fractional time derivative
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).
Physica : europhysics journal ; A, Statistical mechanics and its applications
10.1016/j.physa.2011.12.035
0378-4371
1873-2119
wos:2011-2013
WOS:000301209400003
Tomovski, Z (reprint author), St Cyril & Methodius Univ, Fac Nat Sci & Math, Inst Math, Skopje 1000, Macedonia., tomovski@pmf.ukim.mk; trifce.sandev@drs.gov.mk; metz@ph.tum.de; j.l.a.dubbeldam@tudelft.nl
DAAD; NWO; Academy of Finland; Ministry of Education and Science of the
Republic of Macedonia
Zivorad Tomovski
Trifce Sandev
Ralf Metzler
Johan Dubbeldam
eng
uncontrolled
Fractional diffusion equation
eng
uncontrolled
Composite fractional derivative
eng
uncontrolled
Riesz-Feller fractional derivative
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
Fox H-function
eng
uncontrolled
Fractional moments
eng
uncontrolled
Asymptotic expansions
eng
uncontrolled
Grunwald-Letnikov approximation
Institut für Physik und Astronomie
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