-
2
-
-
0001618393
-
An algorithm for the numeicial solution of differential equations of fractional order
-
K. Dithelm An algorithm for the numeicial solution of differential equations of fractional order Electron. Trans. Numer. Anal. 5 1997 1 6
-
(1997)
Electron. Trans. Numer. Anal.
, vol.5
, pp. 1-6
-
-
Dithelm, K.1
-
3
-
-
0036650479
-
A predictor-corrector approach for the numerical solution of fractional differential equations
-
DOI 10.1023/A:1016592219341, Fractional Order Calculus and Its Applications
-
K. Dithelm, N.J. Ford, and A.D. Freed A predictorcorrector approach for the numerical solution of fractional differential equations Nonlinear Dynam. 29 2002 3 22 (Pubitemid 34945390)
-
(2002)
Nonlinear Dynamics
, vol.29
, Issue.1-4
, pp. 3-22
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
4
-
-
69749102394
-
On the fractional Adams method
-
C.P. Li, and X.H. Dao On the fractional Adams method Comput. Math. Appl. 58 2009 1573 1588
-
(2009)
Comput. Math. Appl.
, vol.58
, pp. 1573-1588
-
-
Li, C.P.1
Dao, X.H.2
-
5
-
-
79952454978
-
Numerical approaches to fractional calculus and fractional ordinary differential equation
-
C.P. Li, A. Chen, and J.J. Ye Numerical approaches to fractional calculus and fractional ordinary differential equation J. Comput. Phys. 230 2011 3352 3368
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 3352-3368
-
-
Li, C.P.1
Chen, A.2
Ye, J.J.3
-
6
-
-
0012820367
-
Solution of non-integer order differential equations via the Adomian decomposition method
-
H.L. Arora, and F.I. Abddwahidi Solution of non-integer order differential equations via the Adomian decomposition method Appl. Math. Lett. 6 1993 21 23
-
(1993)
Appl. Math. Lett.
, vol.6
, pp. 21-23
-
-
Arora, H.L.1
Abddwahidi, F.I.2
-
7
-
-
17444419514
-
The Adomian method applied to some extraordinary differential equations
-
A.J. George, and A. Chakrabarti The Adomian method applied to some extraordinary differential equations Appl. Math. Lett. 8 1993 91 97
-
(1993)
Appl. Math. Lett.
, vol.8
, pp. 91-97
-
-
George, A.J.1
Chakrabarti, A.2
-
8
-
-
35348938590
-
Solving fractional diffusion and wave equations by modified homotopy perturbation method
-
H. Jafari, and S. Momani Solving fractional diffusion and wave equations by modified homotopy perturbation method Phys. Lett. A 370 2007 388 396
-
(2007)
Phys. Lett. A
, vol.370
, pp. 388-396
-
-
Jafari, H.1
Momani, S.2
-
9
-
-
35349007529
-
Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
-
S. Momani, Z. Odibat, and V.S. Erturk Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation Phys. Lett. A 370 2007 379 387
-
(2007)
Phys. Lett. A
, vol.370
, pp. 379-387
-
-
Momani, S.1
Odibat, Z.2
Erturk, V.S.3
-
10
-
-
65049090377
-
Numerical algorithm based on Adomian decomposition for fractional differential equations
-
C.P. Li, and Y.H. Wang Numerical algorithm based on Adomian decomposition for fractional differential equations Comput. Math. Appl. 57 2009 1672 1681
-
(2009)
Comput. Math. Appl.
, vol.57
, pp. 1672-1681
-
-
Li, C.P.1
Wang, Y.H.2
-
12
-
-
28044468843
-
Finite difference approximations for two-sided space-fractional partial differential equations
-
DOI 10.1016/j.apnum.2005.02.008, PII S0168927405000590
-
M.M. Meerschaert, and Charles Tadjeran Finite difference approxiamtion for two-sided space-fractional partial differential equations J. Appl. Math. 56 2006 80 90 (Pubitemid 41690768)
-
(2006)
Applied Numerical Mathematics
, vol.56
, Issue.1
, pp. 80-90
-
-
Meerschaert, M.M.1
Tadjeran, C.2
-
13
-
-
25444472344
-
An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
-
DOI 10.1137/030602666
-
S.B. Yuste, and L. Acedo An explicit finite difference method and a new von Numann-type stability analysis for fractional diffusion equations SIAM J. Numer. Anal. 42 2005 1862 1874 (Pubitemid 41634613)
-
(2005)
SIAM Journal on Numerical Analysis
, vol.42
, Issue.5
, pp. 1862-1874
-
-
Yuste, S.B.1
Acedo, L.2
-
14
-
-
33747605785
-
Hybrid symbolic and numerical simulation studies of time-fractional order wave-diffusion systems
-
DOI 10.1080/00207170600726493, PII R25P69013J741W71
-
J.S. Liang, and Y.Q. Chen Hybrid symbolic and numerical simulation studies of time-fractional order wave-diffusion systems Internat. J. Control 79 2006 1462 1470 (Pubitemid 44267818)
-
(2006)
International Journal of Control
, vol.79
, Issue.11
, pp. 1462-1470
-
-
Liang, J.1
Chen, Y.Q.2
-
15
-
-
33845628108
-
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
-
DOI 10.1016/j.jcp.2006.05.030, PII S0021999106002610
-
C. Tadjeran, and M.M. Meerschaert A second order accurate numerical method for the two-dimensional fractional diffusion equation J. Comput. Phys. 220 2007 813 823 (Pubitemid 44942995)
-
(2007)
Journal of Computational Physics
, vol.220
, Issue.2
, pp. 813-823
-
-
Tadjeran, C.1
Meerschaert, M.M.2
-
16
-
-
67649624652
-
Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems
-
M.S. Tavazoei, M. Haeri, S. Bolouki, and M. Siami Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems SIAM J. Numer. Anal. 47 2008 321 338
-
(2008)
SIAM J. Numer. Anal.
, vol.47
, pp. 321-338
-
-
Tavazoei, M.S.1
Haeri, M.2
Bolouki, S.3
Siami, M.4
-
17
-
-
55549107511
-
New solution and analytical techniques of the implicit numerical method for the sub-diffusion equation
-
P. Zhuang, F. Liu, V. Anh, and I. Turner New solution and analytical techniques of the implicit numerical method for the sub-diffusion equation SIAM J. Numer. Anal. 46 2008 1079 1095
-
(2008)
SIAM J. Numer. Anal.
, vol.46
, pp. 1079-1095
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
-
18
-
-
77958536189
-
A space-time spectral method for the time fractional diffusion equation
-
X.J. Li, and C.J. Xu A space-time spectral method for the time fractional diffusion equation SIAM J. Numer. Anal. 47 2009 2108 2131
-
(2009)
SIAM J. Numer. Anal.
, vol.47
, pp. 2108-2131
-
-
Li, X.J.1
Xu, C.J.2
-
19
-
-
14644446063
-
Least squares finite-element solution of a fractional order two-point boundary value problem
-
DOI 10.1016/j.camwa.2004.10.003, PII S0898122104003438
-
G.J. Fix, and J.P. Roop Least squares finite-element solution of a fractional order two-point boundary value problem Comput. Math. Appl. 48 2004 1017 1033 (Pubitemid 40319749)
-
(2004)
Computers and Mathematics with Applications
, vol.48
, Issue.7-8
, pp. 1017-1033
-
-
Fix, G.J.1
Roof, J.P.2
-
21
-
-
33646262074
-
Variational formulation for the stationary fractional advection dispersion equation
-
V.J. Ervin, and J.P. Roop Variational formulation for the stationary fractional advection dispersion equation Numer. Methods Partial Differential Equations 22 2006 558 576
-
(2006)
Numer. Methods Partial Differential Equations
, vol.22
, pp. 558-576
-
-
Ervin, V.J.1
Roop, J.P.2
-
22
-
-
42649109055
-
Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation
-
DOI 10.1137/050642757
-
V.J. Ervin, N. Heuer, and J.P. Roop Numerical approximation of a time dependent nonlinear, space-fractional diffusion equation SIAM J. Numer. Anal. 45 2007 572 591 (Pubitemid 351599168)
-
(2007)
SIAM Journal on Numerical Analysis
, vol.45
, Issue.2
, pp. 572-591
-
-
Ervin, V.J.1
Heuer, N.2
Roop, J.P.3
-
23
-
-
77958016082
-
Galerkin finite element approximations of symmetric space-fractional partial differential equations
-
H. Zhang, F. Liu, and V. Anh Galerkin finite element approximations of symmetric space-fractional partial differential equations Appl. Math. Comput. 217 2010 2534 2545
-
(2010)
Appl. Math. Comput.
, vol.217
, pp. 2534-2545
-
-
Zhang, H.1
Liu, F.2
Anh, V.3
-
24
-
-
76449122108
-
A note on the finite element method for the space-fractional advection diffusion equation
-
Y.Y. Zheng, C.P. Li, and Z.G. Zhao A note on the finite element method for the space-fractional advection diffusion equation Comput. Math. Appl. 59 2010 1718 1726
-
(2010)
Comput. Math. Appl.
, vol.59
, pp. 1718-1726
-
-
Zheng, Y.Y.1
Li, C.P.2
Zhao, Z.G.3
-
25
-
-
79251585926
-
A fully discrete discontinuous Galerkin method for nonlinear fractional FokkerPlanck equation
-
10.1155/2010/279038 Article ID: 279038
-
Y.Y. Zheng, C.P. Li, and Z.G. Zhao A fully discrete discontinuous Galerkin method for nonlinear fractional FokkerPlanck equation Math. Probl. Eng. 2010 2010 10.1155/2010/279038 Article ID: 279038
-
(2010)
Math. Probl. Eng.
, vol.2010
-
-
Zheng, Y.Y.1
Li, C.P.2
Zhao, Z.G.3
-
26
-
-
79955115806
-
Finite element approximation for the modified anomalous subdiffusion process
-
doi:10.1016/j.apm.2011.02.036
-
Q. Liu, F. Liu, I. Turner, V. Anh, Finite element approximation for the modified anomalous subdiffusion process, Appl. Math. Modelling (2011), in press (doi:10.1016/j.apm.2011.02.036).
-
(2011)
Appl. Math. Modelling
-
-
Liu, Q.1
Liu, F.2
Turner, I.3
Anh, V.4
-
27
-
-
0009481303
-
The fractional diffusion equation
-
W. Wyss The fractional diffusion equation J. Math. Phys. 27 1986 2782 2785
-
(1986)
J. Math. Phys.
, vol.27
, pp. 2782-2785
-
-
Wyss, W.1
-
28
-
-
34250511985
-
A general theory of heat conduction with finite wave speeds
-
M.E. Gurtin, and A.C. Pipkin A general theory of heat conduction with finite wave speeds Arch. Ration. Mech. Anal. 31 1968 113 126
-
(1968)
Arch. Ration. Mech. Anal.
, vol.31
, pp. 113-126
-
-
Gurtin, M.E.1
Pipkin, A.C.2
-
29
-
-
0348114809
-
On second sound in materials with memory
-
P.J. Chen, and M.E. Gurtin On second sound in materials with memory Z. Angew. Math. Phys. 21 1970 232 241
-
(1970)
Z. Angew. Math. Phys.
, vol.21
, pp. 232-241
-
-
Chen, P.J.1
Gurtin, M.E.2
-
30
-
-
0020949678
-
On the thermal transients with finite wave speeds
-
T.B. Moodi, and R.J. Tait On the thermal transients with finite wave speeds Acta Mech. 50 1983 97 104 (Pubitemid 14531018)
-
(1983)
Acta Mechanica
, vol.50
, Issue.1-2
, pp. 97-104
-
-
Moodie, T.B.1
Tait, R.J.2
-
31
-
-
0015397742
-
Transient thermal waves in the general theory of heat conduction with finite wave speeds
-
F.R. Norwood Transient thermal waves in the general theory of heat conduction with finite wave speeds J. Appl. Mech. 39 1972 673 676
-
(1972)
J. Appl. Mech.
, vol.39
, pp. 673-676
-
-
Norwood, F.R.1
-
32
-
-
0027607737
-
Thermoelasticity without energy dissipation
-
A.E. Green, and P.M. Naghdi Thermoelasticity without energy dissipation J. Elasticity 31 1993 189 208 (Pubitemid 23712563)
-
(1993)
Journal of Elasticity
, vol.31
, Issue.3
, pp. 189-208
-
-
Green, A.E.1
Naghdi, P.M.2
-
33
-
-
84973509052
-
Thermoelasticity with second sound: A review
-
D.S. Chandrasekharaiah Thermoelasticity with second sound: a review Appl. Mech. Rev. 39 1986 355 376
-
(1986)
Appl. Mech. Rev.
, vol.39
, pp. 355-376
-
-
Chandrasekharaiah, D.S.1
-
35
-
-
33846862055
-
Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation
-
DOI 10.1016/j.ijsolstr.2006.07.008, PII S0020768306002757
-
Y.Z. Povstenko Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation Int. J. Solids Structure 44 2007 2324 2348 (Pubitemid 46221404)
-
(2007)
International Journal of Solids and Structures
, vol.44
, Issue.7-8
, pp. 2324-2348
-
-
Povstenko, Y.Z.1
-
36
-
-
0034113992
-
The fractional-order governing equation of Levy motion
-
DOI 10.1029/2000WR900032
-
D.A. Benson, S.W. Wheatcraft, and M.M. Meerschaeert The fractional order governing equations of Lévy motion Water Resour. Res. 36 2000 1413 1423 (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
-
37
-
-
0000885234
-
Lévy dynamics of enhanced diffusion: Application to turbulence
-
M.F. Shlesinger, B.J. West, and J. Klafter Lévy dynamics of enhanced diffusion: application to turbulence Phys. Rev. Lett. 58 1987 1100 1103
-
(1987)
Phys. Rev. Lett.
, vol.58
, pp. 1100-1103
-
-
Shlesinger, M.F.1
West, B.J.2
Klafter, J.3
-
38
-
-
0345504868
-
Global and exploding solutions for nonlocal quadratic evolution problems
-
P. Biler, and W.A. Woyczyski Global and exploding solutions for nonlocal quadratic evolution problems SIAM J. Appl. Math. 59 1998 845 869
-
(1998)
SIAM J. Appl. Math.
, vol.59
, pp. 845-869
-
-
Biler, P.1
Woyczyski, W.A.2
-
39
-
-
0026135818
-
Burgers equation with a fractional derivative: Hereditary effects on nonlinear acoustic waves
-
N. Sugimoto Burgers equation with a fractional derivative: hereditary effects on nonlinear acoustic waves J. Fluid Mech. 225 1991 631 653
-
(1991)
J. Fluid Mech.
, vol.225
, pp. 631-653
-
-
Sugimoto, N.1
-
40
-
-
0003598078
-
-
(in Russian)
-
S.C. Samko, A.A. Kilbas, O.I. Maxitchev, Integrals and derivatives of the fractional order and some of their applications, Nauka i Tekhnika, Minsk, 1987 (in Russian).
-
(1987)
Integrals and Derivatives of the Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk
-
-
Samko, S.C.1
Kilbas, A.A.2
Maxitchev, O.I.3
-
41
-
-
84977255207
-
Linear models of dissipation whose Q is almost frequency independent, part II
-
M. Caputo Linear models of dissipation whose Q is almost frequency independent, part II Geophys. J. R. Astron. Soc. 13 1963 529 539
-
(1963)
Geophys. J. R. Astron. Soc.
, vol.13
, pp. 529-539
-
-
Caputo, M.1
-
42
-
-
33745869026
-
Physical interpretation of initial conditons for frational differenial equations with Riemann-Liouville fractionsl derivatives
-
N. Heymans, and I. Podlubny Physical interpretation of initial conditons for frational differenial equations with Riemann-Liouville fractionsl derivatives Rheol. Acta 45 2006 765 772
-
(2006)
Rheol. Acta
, vol.45
, pp. 765-772
-
-
Heymans, N.1
Podlubny, I.2
-
43
-
-
34247212711
-
Remarks on fractional derivatives
-
C.P. Li, and W.H. Deng Remarks on fractional derivatives Appl. Math. Comput. 187 2007 777 784
-
(2007)
Appl. Math. Comput.
, vol.187
, pp. 777-784
-
-
Li, C.P.1
Deng, W.H.2
-
44
-
-
67349121725
-
Fractional derivatives in complex plane
-
C.P. Li, X.H. Dao, and P. Guo Fractional derivatives in complex plane Nonlinear Anal. TMA 71 2009 1857 1869
-
(2009)
Nonlinear Anal. TMA
, vol.71
, pp. 1857-1869
-
-
Li, C.P.1
Dao, X.H.2
Guo, P.3
-
45
-
-
34547548712
-
Finite difference/spectral approximations for the time-fractional diffusion equation
-
Y. Lin, and C.J. Xu Finite difference/spectral approximations for the time-fractional diffusion equation J. Comput. Phys. 225 2007 1533 1552
-
(2007)
J. Comput. Phys.
, vol.225
, pp. 1533-1552
-
-
Lin, Y.1
Xu, C.J.2
-
48
-
-
34249335010
-
Short memory principal and a predictorcorrector approach for fractional differential equations
-
W.H. Deng Short memory principal and a predictorcorrector approach for fractional differential equations J. Comput. Appl. Math. 206 2007 174 188
-
(2007)
J. Comput. Appl. Math.
, vol.206
, pp. 174-188
-
-
Deng, W.H.1
|