-
1
-
-
0020765202
-
A theoretical basis for the application of fractional calculus to viscoelasticity
-
Bagley, R L & Torvik, P. J. [1983] "A theoretical basis for the application of fractional calculus to viscoelasticity," J. Rheol. 27, 201-210
-
(1983)
J. Rheol.
, vol.27
, pp. 201-210
-
-
Bagley, R.L.1
Torvik, P.J.2
-
2
-
-
0038103148
-
Transport in a flashing ratchet in the presence of anomalous diffusion
-
Bao, J D. [2003] "Transport in a flashing ratchet in the presence of anomalous diffusion," Phys. Lett. A 314, 203-208
-
(2003)
Phys. Lett. A
, vol.314
, pp. 203-208
-
-
Bao, J.D.1
-
3
-
-
79951723258
-
Fractional Bloch equation with delay
-
Bhalekar, S., Daftardar-Gejji, V., Baleanu, D & Magin, R. [2011] "Fractional Bloch equation with delay," Comput Math. Appl. 61, 1355-1365
-
(2011)
Comput Math. Appl.
, vol.61
, pp. 1355-1365
-
-
Bhalekar, S.1
Daftardar-Gejji, V.2
Baleanu, D.3
Magin, R.4
-
4
-
-
26444463863
-
Fractional diffusion in inhomogeneous media
-
Chechkin, A. V., Gorenflo, R & Sokolov, I. M. [2005] "Fractional diffusion in inhomogeneous media," J. Phys. A: Math. Gen. 38, L679-L684
-
(2005)
J. Phys. A: Math. Gen
, vol.38
-
-
Chechkin, A.V.1
Gorenflo, R.2
Sokolov, I.M.3
-
5
-
-
0036506044
-
Discretization schemes for fractional-order differentiators and integrators
-
Chen, Y. Q & Moore, K. L. [2002] "Discretization schemes for fractional-order differentiators and integrators," IEEE Trans. Circ. Syst. I: Fund. Theoret. Appl. 49, 363-367
-
(2002)
IEEE Trans. Circ. Syst. I: Fund. Theoret. Appl.
, vol.49
, pp. 363-367
-
-
Chen, Y.Q.1
Moore, K.L.2
-
6
-
-
33745725683
-
A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures
-
Chen, W. [2006] "A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures," Chaos 16, 023126
-
(2006)
Chaos
, vol.16
, pp. 023126
-
-
Chen, W.1
-
7
-
-
36149001420
-
A Fourier method for the fractional diffusion equation describing sub-diffusion
-
Chen, C. M., Liu, F., Turner, I & Anh, V. [2007] "A Fourier method for the fractional diffusion equation describing sub-diffusion," J. Comput. Phys. 227, 886-897
-
(2007)
J. Comput. Phys.
, vol.227
, pp. 886-897
-
-
Chen, C.M.1
Liu, F.2
Turner, I.3
Anh, V.4
-
8
-
-
0346897985
-
Mechanics with variable-order differential operators
-
Coimbra, C. F. M. [2003] "Mechanics with variable-order differential operators," Ann. Phys. (Leipzig) Math. Sci. 12, 692-703
-
(2003)
Ann. Phys. (Leipzig) Math. Sci.
, vol.12
, pp. 692-703
-
-
Coimbra, C.F.M.1
-
9
-
-
69049086472
-
Compact finite difference method for the fractional diffusion equation
-
Cui, M. R. [2009] "Compact finite difference method for the fractional diffusion equation," J. Comput. Phys. 228, 7792-7804
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 7792-7804
-
-
Cui, M.R.1
-
10
-
-
32844473927
-
Concentration-dependent diffusivity and anomalous diffusion: A magnetic resonance imaging study of water ingress in porous zeolite
-
de Azevedo, E. N., de Sousa, P. L., de Souza, R. E., Engelsberg, M., Miranda, M.deN.do N & Silva, M. A. [2006] "Concentration-dependent diffusivity and anomalous diffusion: A magnetic resonance imaging study of water ingress in porous zeolite," Phys. Rev. E 73, 011204
-
(2006)
Phys. Rev. e
, vol.73
, pp. 011204
-
-
De Azevedo, E.N.1
De Sousa, P.L.2
De Souza, R.E.3
Engelsberg, M.4
Miranda, M.5
Den Do, N.6
Silva, M.A.7
-
11
-
-
84880235040
-
Nonlinear phenomena, turbulence, transport: Fractional diffusion in plasma turbulence
-
del-Castillo-Negrete, D., Carreras, B. A & Lynch, V. E. [2004] "Nonlinear phenomena, turbulence, transport: Fractional diffusion in plasma turbulence," Phys. Plasmas 11, 363-367
-
(2004)
Phys. Plasmas
, vol.11
, pp. 363-367
-
-
Del-Castillo-Negrete, D.1
Carreras, B.A.2
Lynch, V.E.3
-
12
-
-
36149001762
-
Numerical algorithm for the time fractional Fokker-Planck equation
-
Deng, W. H. [2007] "Numerical algorithm for the time fractional Fokker-Planck equation," J. Comput. Phys. 227, 1510-1522
-
(2007)
J. Comput. Phys.
, vol.227
, pp. 1510-1522
-
-
Deng, W.H.1
-
13
-
-
4043121080
-
Detailed error analysis for a fractional Adams method
-
Diethelm, K., Ford, N. J & Freed, A. D. [2004] "Detailed error analysis for a fractional Adams method," Numer. Algor. 36, 31-52
-
(2004)
Numer. Algor.
, vol.36
, pp. 31-52
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
14
-
-
79954926078
-
On the numerical solution of spacetime fractional diffusion models
-
Hanert, E. [2011] "On the numerical solution of spacetime fractional diffusion models," Comput. Fluids 46, 33-39
-
(2011)
Comput. Fluids
, vol.46
, pp. 33-39
-
-
Hanert, E.1
-
15
-
-
23044492109
-
Application of differential operator with servo-order function in model of viscoelastic deformation process
-
Ingman, D & Suzdalnitsky, J. [2005] "Application of differential operator with servo-order function in model of viscoelastic deformation process," J. Eng. Mech. 131, 763-767
-
(2005)
J. Eng. Mech.
, vol.131
, pp. 763-767
-
-
Ingman, D.1
Suzdalnitsky, J.2
-
16
-
-
0043026707
-
Statistical physics of dynamic systems with variable memory
-
Kobelev, Ya. L., Kobelev, L. Ya & Klimontovich, Yu. L. [2003] "Statistical physics of dynamic systems with variable memory," Dokl. Phys. 48, 285-289
-
(2003)
Dokl. Phys.
, vol.48
, pp. 285-289
-
-
Kobelev Ya., L.1
Ya., K.L.2
Klimontovich Yu., L.3
-
17
-
-
17144427014
-
The accuracy and stability of an implicit solution method for the fractional diffusion equation
-
Langlands, T. A. M & Henry, B. I. [2005] "The accuracy and stability of an implicit solution method for the fractional diffusion equation," J. Comput. Phys. 205, 719-736
-
(2005)
J. Comput. Phys.
, vol.205
, pp. 719-736
-
-
Langlands, T.A.M.1
Henry, B.I.2
-
18
-
-
1842832060
-
Chaos in Chen's system with a fractional order
-
Li, C. P & Peng, G. J. [2004] "Chaos in Chen's system with a fractional order," Chaos Solit. Fract. 22, 443-450
-
(2004)
Chaos Solit. Fract.
, vol.22
, pp. 443-450
-
-
Li, C.P.1
Peng, G.J.2
-
19
-
-
69749102394
-
On the fractional Adams method
-
Li, C. P & Tao, C. X. [2009] "On the fractional Adams method," Comput. Math. Appl. 58, 1573-1588
-
(2009)
Comput. Math. Appl.
, vol.58
, pp. 1573-1588
-
-
Li, C.P.1
Tao, C.X.2
-
20
-
-
79952454978
-
Numerical approaches to fractional calculus and fractional ordinary differential equation
-
Li, C. P., Chen, A & Ye, J. J. [2011] "Numerical approaches to fractional calculus and fractional ordinary differential equation," J. Comput. Phys. 230, 3352-3368
-
(2011)
J. Comput. Phys.
, vol.230
, pp. 3352-3368
-
-
Li, C.P.1
Chen, A.2
Ye, J.J.3
-
21
-
-
38849098330
-
Sample path properties of fractional Riesz-Bessel field of variable order
-
Lim, S. C & Teo, L. P. [2008] "Sample path properties of fractional Riesz-Bessel field of variable order," J Math. Phys. 49, 013509
-
(2008)
J Math. Phys.
, vol.49
, pp. 013509
-
-
Lim, S.C.1
Teo, L.P.2
-
22
-
-
34547548712
-
Finite difference/spectral approximations for the time-fractional diffusion equation
-
Lin, Y & Xu, C. [2007] "Finite difference/spectral approximations for the time-fractional diffusion equation," J. Comput. Phys. 225, 1533-1552
-
(2007)
J. Comput. Phys.
, vol.225
, pp. 1533-1552
-
-
Lin, Y.1
Xu, C.2
-
23
-
-
67349098149
-
Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
-
Lin, R., Liu, F., Anh, V & Turner, I. [2009] "Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation," Appl. Math. Comput. 212, 435-445
-
(2009)
Appl. Math. Comput.
, vol.212
, pp. 435-445
-
-
Lin, R.1
Liu, F.2
Anh, V.3
Turner, I.4
-
24
-
-
0036650957
-
Variable order and distributed order fractional operators
-
Lorenzo, C. F & Hartley, T. T. [2002] "Variable order and distributed order fractional operators," Nonlin. Dyn. 29, 57-98
-
(2002)
Nonlin. Dyn.
, vol.29
, pp. 57-98
-
-
Lorenzo, C.F.1
Hartley, T.T.2
-
25
-
-
0345448323
-
Numerical methods for the solution of partial differential equations of fractional order
-
Lynch, V. E., Carreras, B. A., del-Castillo-Negrete, D., Ferreira-Mejias, K. M & Hicks, H. R. [2003] "Numerical methods for the solution of partial differential equations of fractional order," J. Comput. Phys. 192, 406-421
-
(2003)
J. Comput. Phys.
, vol.192
, 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
-
27
-
-
38349041965
-
Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation
-
Magin, R. L., Abdullah, O., Baleanu, D & Zhou, X. J. [2008] "Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation," J. Magn. Reson. 190, 255-270
-
(2008)
J. Magn. Reson.
, vol.190
, pp. 255-270
-
-
Magin, R.L.1
Abdullah, O.2
Baleanu, D.3
Zhou, X.J.4
-
28
-
-
4444368867
-
Finite difference approximations for fractional advectiondispersion equations
-
Meerschaert, M. M & Tadjeran, C. [2004] "Finite difference approximations for fractional advectiondispersion equations," J. Comput. Appl. Math. 172, 65-77
-
(2004)
J. Comput. Appl. Math.
, vol.172
, pp. 65-77
-
-
Meerschaert, M.M.1
Tadjeran, C.2
-
29
-
-
0002641421
-
The random walk's guide to anomalous diffusion: A fractional dynamics approach
-
Metzler, R & Klafter, J. [2000] "The random walk's guide to anomalous diffusion: A fractional dynamics approach," Phys. Rep. 339, 1-77
-
(2000)
Phys. Rep.
, vol.339
, pp. 1-77
-
-
Metzler, R.1
Klafter, J.2
-
30
-
-
46049119633
-
Implicit finite difference approximation for time fractional diffusion equations
-
Murio, D. A. [2008] "Implicit finite difference approximation for time fractional diffusion equations," Comput. Math. Appl. 56, 1138-1145
-
(2008)
Comput. Math. Appl.
, vol.56
, pp. 1138-1145
-
-
Murio, D.A.1
-
31
-
-
52349084738
-
Variable order modeling of diffusive-convective effects on the oscillatory flow past a sphere
-
Pedro, H. T. C., Kobayashi, M. H., Pereira, J. M. C & Coimbra, C. F. M. [2008] "Variable order modeling of diffusive-convective effects on the oscillatory flow past a sphere," J. Vib. Contr. 14, 1659-1672
-
(2008)
J. Vib. Contr.
, vol.14
, pp. 1659-1672
-
-
Pedro, H.T.C.1
Kobayashi, M.H.2
Pereira, J.M.C.3
Coimbra, C.F.M.4
-
32
-
-
0032653954
-
Fractional-order systems and PI?D?-controllers
-
Podlubny, I. [1999] "Fractional-order systems and PI?D?-controllers," IEEE Trans. Autom. Contr. 44, 208-214
-
(1999)
IEEE Trans. Autom. Contr.
, vol.44
, pp. 208-214
-
-
Podlubny, I.1
-
33
-
-
61349186917
-
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
-
Podlubny, I., Chechkin, A., Skovranek, T., Chen, Y. Q & Vinagre Jara, B. M. [2009] "Matrix approach to discrete fractional calculus II: Partial fractional differential equations," J. Comput. Phys. 228, 3137-3153
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 3137-3153
-
-
Podlubny, I.1
Chechkin, A.2
Skovranek, T.3
Chen, Y.Q.4
Vinagre Jara, B.M.5
-
34
-
-
0011189482
-
Fractional integration operator of variable order in the Holder space H?(x)
-
Ross, B & Samko, S. G. [1995] "Fractional integration operator of variable order in the Holder space H?(x)," Int. J. Math. Math. Sci. 18, 777-788
-
(1995)
Int. J. Math. Math. Sci.
, vol.18
, pp. 777-788
-
-
Ross, B.1
Samko, S.G.2
-
35
-
-
84948882036
-
Integration and differentiation to a variable fractional order
-
Samko, S. G & Ross, B. [1993] "Integration and differentiation to a variable fractional order," Integr. Trans. Spec. Funct. 1, 277-300
-
(1993)
Integr. Trans. Spec. Funct.
, vol.1
, pp. 277-300
-
-
Samko, S.G.1
Ross, B.2
-
36
-
-
33751019968
-
Anomalous diffusion in Purkinje cell dendrites caused by spines
-
Santamaria, F., Wils, S., de Schutter, E & Augustine, G. J. [2006] "Anomalous diffusion in Purkinje cell dendrites caused by spines," Neuron 52, 635-648
-
(2006)
Neuron
, vol.52
, pp. 635-648
-
-
Santamaria, F.1
Wils, S.2
De Schutter, E.3
Augustine, G.J.4
-
37
-
-
0000902727
-
Generalized viscoelastic models: Their fractional equations with solutions
-
Schiessel, H., Metzler, R., Blumen, A & Nonnenmacher, T. F. [1995] "Generalized viscoelastic models: Their fractional equations with solutions," J. Phys. A: Math. Gen. 28, 6567-6584
-
(1995)
J. Phys. A: Math. Gen.
, vol.28
, pp. 6567-6584
-
-
Schiessel, H.1
Metzler, R.2
Blumen, A.3
Nonnenmacher, T.F.4
-
38
-
-
0001691616
-
Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow
-
Solomon, T. H., Weeks, E. R & Swinney, H. L. [1993] "Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow," Phys. Rev. Lett. 71, 3975-3978
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 3975-3978
-
-
Solomon, T.H.1
Weeks, E.R.2
Swinney, H.L.3
-
39
-
-
68649098514
-
Variableorder fractional differential operators in anomalous diffusion modeling
-
Sun, H. G., Chen, W & Chen, Y. Q. [2009] "Variableorder fractional differential operators in anomalous diffusion modeling," Phys. A 388, 4586-4592
-
(2009)
Phys. A
, vol.388
, pp. 4586-4592
-
-
Sun, H.G.1
Chen, W.2
Chen, Y.Q.3
-
40
-
-
78049351606
-
Randomorder fractional differential equation models
-
Sun, H. G., Chen, Y. Q & Chen, W. [2011] "Randomorder fractional differential equation models," Sign. Process. 91, 525-530
-
(2011)
Sign Process.
, vol.91
, pp. 525-530
-
-
Sun, H.G.1
Chen, Y.Q.2
Chen, W.3
-
41
-
-
31744438550
-
A second order accurate numerical approximation for the fractional diffusion equation
-
Tadjeran, C., Meerschaert, M. M & Scheffler, H. P. [2006] "A second order accurate numerical approximation for the fractional diffusion equation," J. Comput. Phys. 213, 205-213
-
(2006)
J. Comput. Phys.
, vol.213
, pp. 205-213
-
-
Tadjeran, C.1
Meerschaert, M.M.2
Scheffler, H.P.3
-
42
-
-
74349105778
-
Variable order differential equations and diffusion with changing modes
-
Umarov, S & Steinberg, S. [2009] "Variable order differential equations and diffusion with changing modes," Zeitschrift fr Analysis und ihre Anwendungen 28, 431-450
-
(2009)
Zeitschrift Fr Analysis und Ihre Anwendungen
, vol.28
, pp. 431-450
-
-
Umarov, S.1
Steinberg, S.2
-
43
-
-
25444472344
-
An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
-
Yuste, S. B & Acedo, L. [2005] "An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations," SIAM J. Numer. Anal. 42, 1862-1874
-
(2005)
SIAM J. Numer. Anal.
, vol.42
, pp. 1862-1874
-
-
Yuste, S.B.1
Acedo, L.2
-
44
-
-
33646128485
-
Weighted average finite difference methods for fractional diffusion equations
-
Yuste, S. B. [2006] "Weighted average finite difference methods for fractional diffusion equations," J. Comput. Phys. 216, 264-274
-
(2006)
J. Comput. Phys.
, vol.216
, pp. 264-274
-
-
Yuste, S.B.1
-
45
-
-
0036887936
-
Chaos, fractional kinetics, and anomalous transport
-
Zaslavsky, G. M. [2002] "Chaos, fractional kinetics, and anomalous transport," Phys. Rep. 371, 461-580
-
(2002)
Phys. Rep.
, vol.371
, pp. 461-580
-
-
Zaslavsky, G.M.1
-
46
-
-
68949098580
-
A finite difference method for fractional partial differential equation
-
Zhang, Y. [2009] "A finite difference method for fractional partial differential equation," Appl. Math. Comput. 215, 524-529
-
(2009)
Appl. Math. Comput.
, vol.215
, pp. 524-529
-
-
Zhang, Y.1
-
47
-
-
84867978055
-
Implicit difference approximation for the time fractional diffusion equation
-
Zhuang, P & Liu, F. [2006] "Implicit difference approximation for the time fractional diffusion equation," Appl. Math. Comput. 22, 87-99
-
(2006)
Appl. Math. Comput.
, vol.22
, pp. 87-99
-
-
Zhuang, P.1
Liu, F.2
-
48
-
-
84907893973
-
Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term
-
Zhuang, P., Liu, F., Anh, V & Turner, I. [2009] "Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term," SIAM J. Numer. Anal. 47, 1760-1781.
-
(2009)
SIAM J. Numer. Anal.
, vol.47
, pp. 1760-1781
-
-
Zhuang, P.1
Liu, F.2
Anh, V.3
Turner, I.4
|