-
1
-
-
41449095257
-
Numericalsolutionsforfractionalreaction-diffusionequations
-
B. Baeumer, M. Meerschaert, Numerical solutions for fractional reaction-diffusion equations, Comput. Math. Appl., 55 (2008), pp. 2212-2226.
-
(2008)
Comput. Math. Appl.
, vol.55
, pp. 2212-2226
-
-
Baeumer, B.1
Meerschaert, M.2
-
2
-
-
36149001420
-
Fourier method for the fractional diffusion equation describing sub-diffusion
-
Chang-Ming Chen, F. Liu, I. Turner, V. Anh, Fourier method for the fractional diffusion equation describing sub-diffusion, J. Comp. Phys., 227 (2007), pp. 886-897.
-
(2007)
J. Comp. Phys.
, vol.227
, pp. 886-897
-
-
Chen, C.-M.1
Liu, F.2
Turner, I.3
Anh, V.4
-
3
-
-
40849115179
-
Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation
-
Chang-Ming Chen, F. Liu, K. Burrage, Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation, Appl. Math. Comp., 198 (2008), pp. 754-769.
-
(2008)
Appl. Math. Comp.
, vol.198
, pp. 754-769
-
-
Chen, C.-M.1
Liu, F.2
Burrage, K.3
-
4
-
-
52049099584
-
Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives
-
Chang-Ming Chen, F. Liu, V. Anh, Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives, Appl. Math. Comp., 204 (2008), pp. 340-351.
-
(2008)
Appl. Math. Comp.
, vol.204
, pp. 340-351
-
-
Chen, C.-M.1
Liu, F.2
Anh, V.3
-
5
-
-
56949093590
-
A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative
-
Chang-Ming Chen, F. Liu, V. Anh, A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative, J. Comput. Appl. Math., 223 (2009), pp. 777-789.
-
(2009)
J. Comput. Appl. Math.
, vol.223
, pp. 777-789
-
-
Chen, C.-M.1
Liu, F.2
Anh, V.3
-
6
-
-
63949084174
-
A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation
-
Chang-Ming Chen, F. Liu, A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation, J. Appl. Math. Computing, 30 (2009), pp. 219-236.
-
(2009)
J. Appl. Math. Computing
, vol.30
, pp. 219-236
-
-
Chen, C.-M.1
Liu, F.2
-
7
-
-
77950690888
-
Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation
-
Chang-Ming Chen, F. Liu, I. Turner, V. Anh, Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation, Numer. Algorithms, 54 (2010), 1-21.
-
(2010)
Numer. Algorithms
, vol.54
, pp. 1-21
-
-
Chen, C.-M.1
Liu, F.2
Turner, I.3
Anh F, V.4
-
8
-
-
0346897985
-
Mechanicswithvariable-order differential operators
-
C.F.M.Coimbra, Mechanicswithvariable-order differential operators, Annalen der Physik, 12 (2003), pp. 692-703.
-
(2003)
Annalen der Physik
, vol.12
, pp. 692-703
-
-
Coimbra, C.F.M.1
-
9
-
-
67349146657
-
Feller semigroups obtained by variable order subordination
-
K. P. Evans, N. Jacob, Feller semigroups obtained by variable order subordination, Rev. Mat. Comput., 20(2) (2007), pp. 293-307.
-
(2007)
Rev. Mat. Comput.
, vol.20
, Issue.2
, pp. 293-307
-
-
Evans, K.P.1
Jacob, N.2
-
10
-
-
0013118687
-
Pseudo differential operators with variable order of differentiation generating Feller semigroup
-
N. Jacob, H. Leopold, Pseudo differential operators with variable order of differentiation generating Feller semigroup, Integr. Equat. Oper. Th. 17 (1993), pp. 544-553.
-
(1993)
Integr. Equat. Oper. Th.
, vol.17
, pp. 544-553
-
-
Jacob, N.1
Leopold, H.2
-
11
-
-
0013161462
-
On Markov processes generated by pseudo differential operator of variable order
-
K. Kikuchi, A. Negoro, On Markov processes generated by pseudo differential operator of variable order, Osaka J. Math. 34 (1997), pp. 319-335.
-
(1997)
Osaka J. Math.
, vol.34
, pp. 319-335
-
-
Kikuchi, K.1
Negoro, A.2
-
12
-
-
17144427014
-
The accuracy and stability of an implicit solution method for the fractional diffusion equation
-
T. A. M. Langlands, B. I. Henry, The accuracy and stability of an implicit solution method for the fractional diffusion equation, J. Comp. Phys., 205 (2005), pp. 719-736.
-
(2005)
J. Comp. Phys.
, vol.205
, pp. 719-736
-
-
Langlands, T.A.M.1
Henry, B.I.2
-
13
-
-
40549123984
-
Anomalous subdiffusion with multispecies linear reaction dynamics
-
T. A. M. Langlands, B. I. Henry, S. L. Wearne, Anomalous subdiffusion with multispecies linear reaction dynamics, Phys. Rev. E, 77, 021111 (2008).
-
(2008)
Phys. Rev. E
, vol.77
, pp. 021111
-
-
Langlands, T.A.M.1
Henry, B.I.2
Wearne, S.L.3
-
14
-
-
0034355283
-
Embedding of function spaces of variable order of differentiation
-
H. G. Leopold, Embedding of function spaces of variable order of differentiation, Czech. Math. J., 49 (1999), pp. 633-644.
-
(1999)
Czech. Math. J.
, vol.49
, pp. 633-644
-
-
Leopold, H.G.1
-
15
-
-
67349098149
-
Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
-
R. Lin, F. Liu, V. Anh, I. Turner, Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation, Appl. Math. Comput., 212 (2009), pp. 435-445.
-
(2009)
Appl. Math. Comput.
, vol.212
, pp. 435-445
-
-
Lin, R.1
Liu, F.2
Anh, V.3
Turner, I.4
-
16
-
-
34547548712
-
Finite difference/spectral approximation for the time-fractional diffusion equation
-
Y. Lin, C. Xu, Finite difference/spectral approximation for the time-fractional diffusion equation, J. Comp. Phys., 225 (2007), pp. 1533-1552.
-
(2007)
J. Comp. Phys.
, vol.225
, pp. 1533-1552
-
-
Lin, Y.1
Xu, C.2
-
17
-
-
67349231192
-
Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
-
F. Liu, C. Yang, K. Burrage, Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term, J. Comput. Appl. Math., 231 (2009), pp. 160-176.
-
(2009)
J. Comput. Appl. Math.
, vol.231
, pp. 160-176
-
-
Liu, F.1
Yang, C.2
Burrage, K.3
-
18
-
-
34547673244
-
Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
-
F. Liu, P. Zhang, V. Anh, K. Burrage, Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation, Appl. Math. Comput., 191 (2007), pp. 12-20.
-
(2007)
Appl. Math. Comput.
, vol.191
, pp. 12-20
-
-
Liu, F.1
Zhang, P.2
Anh, V.3
Burrage, K.4
-
19
-
-
33846798041
-
Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method
-
Q. Liu, F. Liu, I. Turner, V. Anh, Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method, J. Comp. Phys., 222 (2007), pp. 57-70.
-
(2007)
J. Comp. Phys.
, vol.222
, pp. 57-70
-
-
Liu, Q.1
Liu, F.2
Turner, I.3
Anh, V.4
-
21
-
-
0036650957
-
Variable-order and distributed order fractional operators
-
C. F. Lorenzo, T. T. Hartley, Variable-order and distributed order fractional operators, Non- linear Dyn. 29 (2002), pp. 57-98.
-
(2002)
Non-linear Dyn
, vol.29
, pp. 57-98
-
-
Lorenzo, C.F.1
Hartley, T.T.2
-
22
-
-
32444441271
-
The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants
-
M. Meerschaert, A. Zoia, The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants, Ann. Nucl. Energy, 33 (2006), pp. 223-235.
-
(2006)
Ann. Nucl. Energy
, vol.33
, pp. 223-235
-
-
Meerschaert, M.1
Zoia, A.2
-
23
-
-
25444463578
-
Finite difference methods for two-dimensional fractional dispersion equation
-
M. Meerschaert, H.-P. Scheffler, C. Tadjeran, Finite difference methods for two-dimensional fractional dispersion equation, J. Comp. Phys., 211 (2006), pp 249-261.
-
(2006)
J. Comp. Phys.
, vol.211
, pp. 249-261
-
-
Meerschaert, M.1
Scheffler, H.-P.2
Tadjeran, C.3
-
24
-
-
33845628108
-
A second-order accurate numerical method for the two- dimensional fractional diffusion equation
-
C. Tadjeran, M. Meerschaert, A second-order accurate numerical method for the two- dimensional fractional diffusion equation, J. Comp. Phys., 220 (2007), pp, 813-823.
-
(2007)
J. Comp. Phys.
, vol.220
, pp. 813-823
-
-
Tadjeran, C.1
Meerschaert, M.2
-
26
-
-
34547624283
-
Variable order constitutive relation for viscoelasticity
-
L. E. S. Ramirez, C. F. M. Coimbra, Variable order constitutive relation for viscoelasticity, Annalen der Physik, 16 (2007), pp. 543-552.
-
(2007)
Annalen der Physik
, vol.16
, pp. 543-552
-
-
Ramirez, L.E.S.1
Coimbra, C.F.M.2
-
27
-
-
0345381769
-
Anomalous subdiffusion in heterogeneous lipid bilayers
-
T. V. Ratto, M. L. Longo, Anomalous subdiffusion in heterogeneous lipid bilayers, Langmuir, 19 (2003), pp, 1788-1793.
-
(2003)
Langmuir
, vol.19
, pp. 1788-1793
-
-
Ratto, T.V.1
Longo, M.L.2
-
28
-
-
2442585557
-
Fractional generalized random fields of variable order
-
M. D. Ruiz-Medina, V. V. Anh, J. M. Angulo, Fractional generalized random fields of variable order, Stoch. Anal. Appl., 22(2) (2004), pp. 775-799.
-
(2004)
Stoch. Anal. Appl.
, vol.22
, Issue.2
, pp. 775-799
-
-
Ruiz-Medina, M.D.1
Anh, V.V.2
Angulo, J.M.3
-
29
-
-
84948882036
-
Integration and differentiation to a variable fractional order
-
S. G. Samko, B. Ross, Integration and differentiation to a variable fractional order, Integr. Transf. Spec. F., 1 (1993), pp. 277-300.
-
(1993)
Integr. Transf. Spec. F.
, vol.1
, pp. 277-300
-
-
Samko, S.G.1
Ross, B.2
-
30
-
-
0034805503
-
Anomalous subdiffusion in fluorescence photobleaching recovery: A Monte Carlo study
-
M. J. Saxton, Anomalous subdiffusion in fluorescence photobleaching recovery: A Monte Carlo study, Biophys. J., 81 (2001), pp. 2226-2240.
-
(2001)
Biophys. J.
, vol.81
, pp. 2226-2240
-
-
Saxton, M.J.1
-
31
-
-
2342630824
-
Anomalous subdiffusion of proteins and lipids in membranes observed by fluorescence correlation spectroscopy
-
P. Schwille, J. Korlach, W. W. Webb, Anomalous subdiffusion of proteins and lipids in membranes observed by fluorescence correlation spectroscopy, Biophys. J., 76 (1999), A391- A391.
-
(1999)
Biophys. J.
, vol.76
-
-
Schwille, P.1
Korlach, J.2
Webb, W.W.3
-
32
-
-
25444483399
-
Variable viscoelasticity operator
-
C.M.Soon,C.F.M.Coimbra,M.H.Kobayashi, Variable viscoelasticity operator, Annalen der Physik, 14 (2005), pp. 378-389.
-
(2005)
Annalen der Physik
, vol.14
, pp. 378-389
-
-
Soon, C.M.1
Coimbra, C.F.M.2
Kobayashi, M.H.3
-
33
-
-
35648947830
-
An anomalous subdiffusion model for calcium spark in cardiac myocytes
-
doi:10.1063/1.2805208
-
W. Tan, Chaoqi Fu, Ceji Fu, An anomalous subdiffusion model for calcium spark in cardiac myocytes, Appl. Phys. Lett. 91, 183901 (2007), doi:10.1063/1.2805208.
-
(2007)
Appl. Phys. Lett.
, vol.91
, pp. 183901
-
-
Tan, W.1
Fu, C.2
Fu, C.3
-
34
-
-
14844331313
-
Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells
-
M. Weiss, M. Elsner, F. Kartberg, T. Nilsson, Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells, Biophys. J., 87 (2004), pp. 3518-3524.
-
(2004)
Biophys. J.
, vol.87
, pp. 3518-3524
-
-
Weiss, M.1
Elsner, M.2
Kartberg, F.3
Nilsson, T.4
-
35
-
-
41449094744
-
Solving linear and non-linear space-time fractional reaction-diffusion equations by the Adomian decomposition method
-
Q. Yu, F. Liu, V. Anh, I. Turner, Solving linear and non-linear space-time fractional reaction- diffusion equations by the Adomian decomposition method, Int. J. Numer. Meth. Eng., 74 (2008), pp. 138-158.
-
(2008)
Int. J. Numer. Meth. Eng.
, vol.74
, pp. 138-158
-
-
Yu, Q.1
Liu, F.2
Anh, V.3
Turner, I.4
-
36
-
-
25444472344
-
An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations
-
S. B. Yuste, L. Acedo, An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations, SIAM J. Numer. Anal., 42 (5) (2005), pp. 1862-1874.
-
(2005)
SIAM J. Numer. Anal.
, vol.42
, Issue.5
, pp. 1862-1874
-
-
Yuste, S.B.1
Acedo, L.2
-
37
-
-
33646128485
-
Weighted average finite difference methods for fractional diffusion equations
-
S. B. Yuste, Weighted average finite difference methods for fractional diffusion equations, J. Comp. Phys., 216 (2006), pp. 264-274.
-
(2006)
J. Comp. Phys.
, vol.216
, pp. 264-274
-
-
Yuste, S.B.1
-
38
-
-
34548553258
-
Implicit difference approximation for the two-dimensional space-time fractional diffusion equation
-
P. Zhuang, F. Liu, Implicit difference approximation for the two-dimensional space-time fractional diffusion equation, J. Appl. Math. Computing, 25 (2007), pp. 269-282.
-
(2007)
J. Appl. Math. Computing
, vol.25
, pp. 269-282
-
-
Zhuang, P.1
Liu, F.2
-
39
-
-
84907893973
-
Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term
-
P. Zhuang, F. Liu, V. Anh, I. Turner, Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term, SIAM J. Numer. Anal., 47 (2009), pp. 1760-1781.
-
(2009)
SIAM J. Numer. Anal.
, vol.47
, pp. 1760-1781
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
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