-
2
-
-
0034032484
-
Application of a fractional advection-dispersion equation
-
DOI 10.1029/2000WR900031
-
Benson D. A., Wheatcraft S. W., Meerschaert M. M., Application of a fractional advection-dispersion equation. Water Resources Research 2000 36 6 1403 1412 2-s2.0-0028669983 10.1029/2000WR900031 (Pubitemid 30334241)
-
(2000)
Water Resources Research
, vol.36
, Issue.6
, pp. 1403-1412
-
-
Benson, D.A.1
Wheatcraft, S.W.2
Meerschaert, M.M.3
-
3
-
-
0034113992
-
The fractional-order governing equation of Levy motion
-
DOI 10.1029/2000WR900032
-
Benson D. A., Wheatcraft S. W., Meerschaert M. M., The fractional-order governing equation of Lévy motion. Water Resources Research 2000 36 6 1413 1423 10.1029/2000WR900032 (Pubitemid 30334242)
-
(2000)
Water Resources Research
, vol.36
, Issue.6
, pp. 1413-1423
-
-
Benson, D.A.1
Wheatcraft, S.W.2
Meerschaert, M.M.3
-
4
-
-
0040307478
-
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
-
10.1016/0370-1573(90)90099-N MR1081295
-
Bouchaud J.-P., Georges A., Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Physics Reports 1990 195 4-5 127 293 10.1016/0370-1573(90)90099-N MR1081295
-
(1990)
Physics Reports
, vol.195
, Issue.4-5
, pp. 127-293
-
-
Bouchaud, J.-P.1
Georges, A.2
-
5
-
-
0034205221
-
Fractional Fokker-Planck equation: Dispersive transport in an external force field
-
2-s2.0-0001482546 10.1016/S0167-7322(99)00143-9
-
Metzler R., Klafter J., Fractional Fokker-Planck equation: dispersive transport in an external force field. Journal of Molecular Liquids 2000 86 1 219 228 2-s2.0-0001482546 10.1016/S0167-7322(99)00143-9
-
(2000)
Journal of Molecular Liquids
, vol.86
, Issue.1
, pp. 219-228
-
-
Metzler, R.1
Klafter, J.2
-
6
-
-
0036887936
-
Chaos, fractional kinetics, and anomalous transport
-
10.1016/S0370-1573(02)00331-9 MR1937584 ZBL0999.82053
-
Zaslavsky G. M., Chaos, fractional kinetics, and anomalous transport. Physics Reports 2002 371 6 461 580 10.1016/S0370-1573(02)00331-9 MR1937584 ZBL0999.82053
-
(2002)
Physics Reports
, vol.371
, Issue.6
, pp. 461-580
-
-
Zaslavsky, G.M.1
-
7
-
-
1542425102
-
Numerical solution of the space fractional Fokker-Planck equation
-
DOI 10.1016/j.cam.2003.09.028, PII S0377042703008616
-
Liu F., Anh V., Turner I., Numerical solution of the space fractional Fokker-Planck equation. Journal of Computational and Applied Mathematics 2004 166 1 209 219 2-s2.0-0035538580 MR2057973 10.1016/j.cam.2003.09.028 ZBL1036.82019 (Pubitemid 38342127)
-
(2004)
Journal of Computational and Applied Mathematics
, vol.166
, Issue.1
, pp. 209-219
-
-
Liu, F.1
Anh, V.2
Turner, I.3
-
8
-
-
0000361678
-
Random walk models for space-fractional diffusion processes
-
MR1656314 ZBL0946.60039
-
Gorenflo R., Mainardi F., Random walk models for space-fractional diffusion processes. Fractional Calculus & Applied Analysis 1998 1 2 167 191 MR1656314 ZBL0946.60039
-
(1998)
Fractional Calculus & Applied Analysis
, vol.1
, Issue.2
, pp. 167-191
-
-
Gorenflo, R.1
Mainardi, F.2
-
9
-
-
3342977216
-
Fokker-Planck equation and subdiffusive fractional Fokker-Planck equation of bistable systems with sinks
-
10.1016/j.physa.2004.04.114 MR2092678
-
Chow C. W., Liu K. L., Fokker-Planck equation and subdiffusive fractional Fokker-Planck equation of bistable systems with sinks. Physica A 2004 341 1-4 87 106 10.1016/j.physa.2004.04.114 MR2092678
-
(2004)
Physica A
, vol.341
, Issue.1-4
, pp. 87-106
-
-
Chow, C.W.1
Liu, K.L.2
-
10
-
-
25444472344
-
An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
-
DOI 10.1137/030602666
-
Yuste S. B., Acedo L., An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations. SIAM Journal on Numerical Analysis 2005 42 5 1862 1874 10.1137/030602666 MR2139227 ZBL1119.65379 (Pubitemid 41634613)
-
(2005)
SIAM Journal on Numerical Analysis
, vol.42
, Issue.5
, pp. 1862-1874
-
-
Yuste, S.B.1
Acedo, L.2
-
11
-
-
17144427014
-
The accuracy and stability of an implicit solution method for the fractional diffusion equation
-
DOI 10.1016/j.jcp.2004.11.025, PII S0021999104004887
-
Langlands T. A. M., Henry B. I., The accuracy and stability of an implicit solution method for the fractional diffusion equation. Journal of Computational Physics 2005 205 2 719 736 MR2135000 10.1016/j.jcp.2004.11.025 ZBL1072.65123 (Pubitemid 40518394)
-
(2005)
Journal of Computational Physics
, vol.205
, Issue.2
, pp. 719-736
-
-
Langlands, T.A.M.1
Henry, B.I.2
-
12
-
-
36149001420
-
A Fourier method for the fractional diffusion equation describing sub-diffusion
-
MR2442379 10.1016/j.jcp.2007.05.012 ZBL1165.65053
-
Chen C.-M., Liu F., Turner I., Anh V., A Fourier method for the fractional diffusion equation describing sub-diffusion. Journal of Computational Physics 2007 227 2 886 897 MR2442379 10.1016/j.jcp.2007.05.012 ZBL1165.65053
-
(2007)
Journal of Computational Physics
, vol.227
, Issue.2
, pp. 886-897
-
-
Chen, C.-M.1
Liu, F.2
Turner, I.3
Anh, V.4
-
13
-
-
55549107511
-
New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation
-
MR2383224 10.1137/060673114
-
Zhuang P., Liu F., Anh V., Turner I., New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. SIAM Journal on Numerical Analysis 2008 46 2 1079 1095 MR2383224 10.1137/060673114
-
(2008)
SIAM Journal on Numerical Analysis
, vol.46
, Issue.2
, pp. 1079-1095
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
-
14
-
-
56949093590
-
A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative
-
MR2478879 10.1016/j.cam.2008.03.001 ZBL1153.76049
-
Chen C.-M., Liu F., Anh V., A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative. Journal of Computational and Applied Mathematics 2009 223 2 777 789 MR2478879 10.1016/j.cam.2008.03.001 ZBL1153.76049
-
(2009)
Journal of Computational and Applied Mathematics
, vol.223
, Issue.2
, pp. 777-789
-
-
Chen, C.-M.1
Liu, F.2
Anh, V.3
-
15
-
-
51749116733
-
Finite difference approximations for the fractional Fokker-Planck equation
-
10.1016/j.apm.2007.11.005 MR2458510 ZBL1167.65419
-
Chen S., Liu F., Zhuang P., Anh V., Finite difference approximations for the fractional Fokker-Planck equation. Applied Mathematical Modelling 2009 33 1 256 273 10.1016/j.apm.2007.11.005 MR2458510 ZBL1167.65419
-
(2009)
Applied Mathematical Modelling
, vol.33
, Issue.1
, pp. 256-273
-
-
Chen, S.1
Liu, F.2
Zhuang, P.3
Anh, V.4
-
16
-
-
77951470147
-
-
New York, NY, USA Academic Press Mathematics in Science and Engineering MR1658022
-
Podlubny I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications 1999 198 New York, NY, USA Academic Press xxiv+340 Mathematics in Science and Engineering MR1658022
-
(1999)
Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications
, vol.198
-
-
Podlubny, I.1
-
17
-
-
34249040591
-
Fractional diffusion equation with an absorbent term and a linear external force: Exact solution
-
2-s2.0-17744391775 10.1016/j.physleta.2007.02.056
-
Schot A., Lenzi M. K., Evangelista L. R., Malacarne L. C., Mendes R. S., Lenzi E. K., Fractional diffusion equation with an absorbent term and a linear external force: exact solution. Physics Letters A 2007 366 4-5 346 350 2-s2.0-17744391775 10.1016/j.physleta.2007.02.056
-
(2007)
Physics Letters A
, vol.366
, Issue.4-5
, pp. 346-350
-
-
Schot, A.1
Lenzi, M.K.2
Evangelista, L.R.3
Malacarne, L.C.4
Mendes, R.S.5
Lenzi, E.K.6
-
18
-
-
0037365591
-
Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions
-
2-s2.0-0036828775 10.1016/S0378-4371(02)01495-4 ZBL1008.82027
-
Lenzi E. K., Malacarne L. C., Mendes R. S., Pedron I. T., Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions. Physica A 2003 319 245 252 2-s2.0-0036828775 10.1016/S0378-4371(02)01495-4 ZBL1008.82027
-
(2003)
Physica A
, vol.319
, pp. 245-252
-
-
Lenzi, E.K.1
Malacarne, L.C.2
Mendes, R.S.3
Pedron, I.T.4
-
19
-
-
84901918366
-
Numerical treatment for the fractional Fokker-Planck equation
-
MR2366327
-
Zhuang P., Liu F., Anh V., Turner I., Numerical treatment for the fractional Fokker-Planck equation. The ANZIAM Journal 2006-2007 48 C759 C774 MR2366327
-
(2006)
The ANZIAM Journal
, vol.48
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
-
20
-
-
41449095257
-
Numerical solutions for fractional reaction-diffusion equations
-
MR2413687 10.1016/j.camwa.2007.11.012 ZBL1142.65422
-
Baeumer B., Kovács M., Meerschaert M. M., Numerical solutions for fractional reaction-diffusion equations. Computers & Mathematics with Applications 2008 55 10 2212 2226 MR2413687 10.1016/j.camwa.2007.11.012 ZBL1142.65422
-
(2008)
Computers & Mathematics with Applications
, vol.55
, Issue.10
, pp. 2212-2226
-
-
Baeumer, B.1
Kovács, M.2
Meerschaert, M.M.3
-
22
-
-
28044468843
-
Finite difference approximations for two-sided space-fractional partial differential equations
-
DOI 10.1016/j.apnum.2005.02.008, PII S0168927405000590
-
Meerschaert M. M., Tadjeran C., Finite difference approximations for two-sided space-fractional partial differential equations. Applied Numerical Mathematics 2006 56 1 80 90 MR2186432 10.1016/j.apnum.2005.02.008 ZBL1086.65087 (Pubitemid 41690768)
-
(2006)
Applied Numerical Mathematics
, vol.56
, Issue.1
, pp. 80-90
-
-
Meerschaert, M.M.1
Tadjeran, C.2
-
23
-
-
33751545053
-
Fractional high order methods for the nonlinear fractional ordinary differential equation
-
DOI 10.1016/j.na.2005.12.027, PII S0362546X05010503
-
Lin R., Liu F., Fractional high order methods for the nonlinear fractional ordinary differential equation. Nonlinear Analysis: Theory, Methods & Applications 2007 66 4 856 869 10.1016/j.na.2005.12.027 MR2288436 ZBL1118.65079 (Pubitemid 44839109)
-
(2007)
Nonlinear Analysis, Theory, Methods and Applications
, vol.66
, Issue.4
, pp. 856-869
-
-
Lin, R.1
Liu, F.2
-
24
-
-
67349231192
-
Numerical method and analytic technique of the modified anomalous subdiffusion equation with a nonlinear source term
-
MR2532659 10.1016/j.cam.2009.02.013
-
Liu F., Yang C., Burrage K., Numerical method and analytic technique of the modified anomalous subdiffusion equation with a nonlinear source term. Journal of Computational and Applied Mathematics 2009 231 1 160 176 MR2532659 10.1016/j.cam.2009.02.013
-
(2009)
Journal of Computational and Applied Mathematics
, vol.231
, Issue.1
, pp. 160-176
-
-
Liu, F.1
Yang, C.2
Burrage, K.3
-
25
-
-
4444368867
-
Finite difference approximations for fractional advection-dispersion flow equations
-
DOI 10.1016/j.cam.2004.01.033, PII S0377042704000986
-
Meerschaert M. M., Tadjeran C., Finite difference approximations for fractional advection-dispersion flow equations. Journal of Computational and Applied Mathematics 2004 172 1 65 77 MR2091131 10.1016/j.cam.2004.01.033 ZBL1126.76346 (Pubitemid 39204390)
-
(2004)
Journal of Computational and Applied Mathematics
, vol.172
, Issue.1
, pp. 65-77
-
-
Meerschaert, M.M.1
Tadjeran, C.2
-
26
-
-
59349113701
-
Finite element method for the space and time fractional Fokker-Planck equation
-
10.1137/080714130 MR2452858
-
Deng W., Finite element method for the space and time fractional Fokker-Planck equation. SIAM Journal on Numerical Analysis 2008-2009 47 1 204 226 10.1137/080714130 MR2452858
-
(2008)
SIAM Journal on Numerical Analysis
, vol.47
, Issue.1
, pp. 204-226
-
-
Deng, W.1
-
27
-
-
33751229020
-
Damping characteristics of finite difference methods for one-dimensional reaction-diffusion equations
-
DOI 10.1016/j.amc.2006.04.023, PII S0096300306003699
-
Ramos J. I., Damping characteristics of finite difference methods for one-dimensional reaction-diffusion equations. Applied Mathematics and Computation 2006 182 1 607 609 MR2292071 10.1016/j.amc.2006.04.023 ZBL1107.65076 (Pubitemid 44781034)
-
(2006)
Applied Mathematics and Computation
, vol.182
, Issue.1
, pp. 607-609
-
-
Ramos, J.I.1
-
28
-
-
0043210605
-
Front dynamics in reaction-diffusion systems with Levy flights: A fractional diffusion approach
-
018302 10.1103/PhysRevLett.91.018302 2-s2.0-3743079140
-
del-Castillo-Negrete D., Carreras B. A., Lynch V. E., Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach. Physical Review Letters 2003 91 1 4 018302 10.1103/PhysRevLett.91.018302 2-s2.0-3743079140
-
(2003)
Physical Review Letters
, vol.91
, Issue.1
, pp. 4
-
-
Del-Castillo-Negrete, D.1
Carreras, B.A.2
Lynch, V.E.3
-
29
-
-
0345448323
-
Numerical methods for the solution of partial differential equations of fractional order
-
DOI 10.1016/j.jcp.2003.07.008
-
Lynch V. E., Carreras B. A., del-Castillo-Negrete D., Ferreira-Mejias K. M., Hicks H. R., Numerical methods for the solution of partial differential equations of fractional order. Journal of Computational Physics 2003 192 2 406 421 MR2020744 10.1016/j.jcp.2003.07.008 ZBL1047.76075 (Pubitemid 37445638)
-
(2003)
Journal of Computational Physics
, vol.192
, Issue.2
, pp. 406-421
-
-
Lynch, V.E.1
Carreras, B.A.2
Del-Castillo-Negrete, D.3
Ferreira-Mejias, K.M.4
Hicks, H.R.5
-
30
-
-
34548677557
-
Fractional reproduction-dispersal equations and heavy tail dispersal kernels
-
DOI 10.1007/s11538-007-9220-2
-
Baeumer B., Kovács M., Meerschaert M. M., Fractional reproduction-dispersal equations and heavy tail dispersal kernels. Bulletin of Mathematical Biology 2007 69 7 2281 2297 MR2341872 10.1007/s11538-007-9220-2 (Pubitemid 47415554)
-
(2007)
Bulletin of Mathematical Biology
, vol.69
, Issue.7
, pp. 2281-2297
-
-
Baeumer, B.1
Kovacs, M.2
Meerschaert, M.M.3
|