35967
2012
2012
eng
2527
2542
16
8
391
article
Elsevier
Amsterdam
1
--
--
--
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 (print)
1873-2119 (online)
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
Referiert
38715
2015
2015
eng
1006
1038
33
4
18
article
De Gruyter
Berlin
1
--
--
--
Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel
We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
Fractional calculus and applied analysis : an international journal for theory and applications
10.1515/fca-2015-0059
1311-0454 (print)
1314-2224 (online)
wos:2015
WOS:000359161800010
Sandev, T (reprint author), Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany., sandev@pks.mpg.de; chechkin@pks.mpg.de; kantz@pks.mpg.de; rmetzler@uni-potsdam.de
IMU Berlin Einstein Foundation; Academy of Finland within the FiDiPro
programme
Trifce Sandev
Aleksei V. Chechkin
Holger Kantz
Ralf Metzler
eng
uncontrolled
continuous time random walk (CTRW)
eng
uncontrolled
Fokker-Planck-Smoluchowski equation
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
multi-scaling
Institut für Physik und Astronomie
Referiert