-
2
-
-
0000078998
-
From continuous time random walks to the fractional Fokker-Planck equation
-
Barkai E., Metzler R., and Klafter J. From continuous time random walks to the fractional Fokker-Planck equation. Phys. Rev. E 61 (2000) 132-138
-
(2000)
Phys. Rev. E
, vol.61
, pp. 132-138
-
-
Barkai, E.1
Metzler, R.2
Klafter, J.3
-
3
-
-
0035305938
-
Fractional Fokker-Planck equation, solution, and application
-
Barkai E. Fractional Fokker-Planck equation, solution, and application. Phys. Rev. E 63 (2001) 046118
-
(2001)
Phys. Rev. E
, vol.63
, pp. 046118
-
-
Barkai, E.1
-
4
-
-
0040307478
-
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
-
Bouchaud J., and Georges A. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications. Phys. Rep. 195 (1990) 127-293
-
(1990)
Phys. Rep.
, vol.195
, pp. 127-293
-
-
Bouchaud, J.1
Georges, A.2
-
6
-
-
34249335010
-
Short memory principle and a predictor-corrector approach for fractional differential equations
-
Deng W.H. Short memory principle and a predictor-corrector 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
-
7
-
-
33846056956
-
Design of multi-directional multi-scroll chaotic attractors based on fractional differential systems via switching control
-
Deng W.H., and Lü J.H. Design of multi-directional multi-scroll chaotic attractors based on fractional differential systems via switching control. Chaos 16 (2006) 043120
-
(2006)
Chaos
, vol.16
, pp. 043120
-
-
Deng, W.H.1
Lü, J.H.2
-
8
-
-
36149000960
-
Generating 3-D scroll grid attractors of fractional differential systems via stair function
-
Deng W.H. Generating 3-D scroll grid attractors of fractional differential systems via stair function. Int. J. Bifurcation Chaos Appl. Sci. Eng. 17 (2007) 1-19
-
(2007)
Int. J. Bifurcation Chaos Appl. Sci. Eng.
, vol.17
, pp. 1-19
-
-
Deng, W.H.1
-
9
-
-
33947133956
-
Stability analysis of linear fractional differential system with multiple time-delays
-
Deng W.H., Li C.P., and Lü J.H. Stability analysis of linear fractional differential system with multiple time-delays. Nonlinear Dynam. 48 (2007) 409-416
-
(2007)
Nonlinear Dynam.
, vol.48
, pp. 409-416
-
-
Deng, W.H.1
Li, C.P.2
Lü, J.H.3
-
10
-
-
34247866598
-
Generalized synchronization in fractional order systems
-
Deng W.H. Generalized synchronization in fractional order systems. Phys. Rev. E 75 (2007) 056201
-
(2007)
Phys. Rev. E
, vol.75
, pp. 056201
-
-
Deng, W.H.1
-
11
-
-
0037081673
-
Analysis of fractional differential equations
-
Diethelm K., and Ford N.J. Analysis of fractional differential equations. J. Math. Anal. Appl. 265 (2002) 229-248
-
(2002)
J. Math. Anal. Appl.
, vol.265
, pp. 229-248
-
-
Diethelm, K.1
Ford, N.J.2
-
12
-
-
0036650479
-
A predictor-corrector approach for the numerical solution of fractional differential equations
-
Diethelm K., Ford N.J., and Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam. 29 (2002) 3-22
-
(2002)
Nonlinear Dynam.
, vol.29
, pp. 3-22
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
13
-
-
4043121080
-
Detailed error analysis for a fractional Adams method
-
Diethelm K., Ford N.J., and Freed A.D. Detailed error analysis for a fractional Adams method. Numer. Algorithms 36 (2004) 31-52
-
(2004)
Numer. Algorithms
, vol.36
, pp. 31-52
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
14
-
-
0035625795
-
The numerical solution of fractional differential equations: Speed versus accuracy
-
Ford N.J., and Simpson A.C. The numerical solution of fractional differential equations: Speed versus accuracy. Numer. Algorithms 26 (2001) 336-346
-
(2001)
Numer. Algorithms
, vol.26
, pp. 336-346
-
-
Ford, N.J.1
Simpson, A.C.2
-
15
-
-
33344478864
-
Current and universal scaling in anomalous transport
-
Goychuk I., Heinsalu E., Patriarca M., Schmid G., and Hänggi P. Current and universal scaling in anomalous transport. Phys. Rev. E 73 (2006) 020101
-
(2006)
Phys. Rev. E
, vol.73
, pp. 020101
-
-
Goychuk, I.1
Heinsalu, E.2
Patriarca, M.3
Schmid, G.4
Hänggi, P.5
-
17
-
-
33646360565
-
Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
-
Heinsalu E., Patriarca M., Goychuk I., Schmid G., and Hänggi P. Fractional Fokker-Planck dynamics: Numerical algorithm and simulations. Phys. Rev. E 73 (2006) 046133
-
(2006)
Phys. Rev. E
, vol.73
, pp. 046133
-
-
Heinsalu, E.1
Patriarca, M.2
Goychuk, I.3
Schmid, G.4
Hänggi, P.5
-
18
-
-
33845888181
-
Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
-
Heymans N., and Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheol. Acta 37 (2005) 1-7
-
(2005)
Rheol. Acta
, vol.37
, pp. 1-7
-
-
Heymans, N.1
Podlubny, I.2
-
19
-
-
0010178279
-
An analog simulation of noninteger order transfer functions for analysis of electrode processes
-
Ichise M., Nagayanagi Y., and Kojima T. An analog simulation of noninteger order transfer functions for analysis of electrode processes. J. Electroanal. Chem. 33 (1971) 253-265
-
(1971)
J. Electroanal. Chem.
, vol.33
, pp. 253-265
-
-
Ichise, M.1
Nagayanagi, Y.2
Kojima, T.3
-
20
-
-
21144479789
-
A Fokker-Planck equation of fractional order with respect to time
-
Jumarie G. A Fokker-Planck equation of fractional order with respect to time. J. Math. Phys. 33 (1992) 3536-3542
-
(1992)
J. Math. Phys.
, vol.33
, pp. 3536-3542
-
-
Jumarie, G.1
-
22
-
-
33645165534
-
Application of fractional calculus to the theory of viscoelasticity
-
Koeller R.C. Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mech. (1984) 229-307
-
(1984)
J. Appl. Mech.
, pp. 229-307
-
-
Koeller, R.C.1
-
23
-
-
0000378977
-
Quantum levy processes and fractional kinetics
-
Kusnezov D., Bulgac A., and Dang G.D. Quantum levy processes and fractional kinetics. Phys. Rev. Lett. 82 (1999) 1136-1139
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 1136-1139
-
-
Kusnezov, D.1
Bulgac, A.2
Dang, G.D.3
-
24
-
-
0038076411
-
Fractional derivatives and special functions
-
Lavoie J.L., Osler T.J., and Tremblay R. Fractional derivatives and special functions. SIAM Rev. 18 (1976) 240-268
-
(1976)
SIAM Rev.
, vol.18
, pp. 240-268
-
-
Lavoie, J.L.1
Osler, T.J.2
Tremblay, R.3
-
25
-
-
0037908922
-
Anomalous diffusion: Fractional Fokker-Planck equation and its solutions
-
Lenzi E.K., Mendes R.S., Fa K.S., and Malacarne L.C. Anomalous diffusion: Fractional Fokker-Planck equation and its solutions. J. Math. Phys. 44 (2003) 2179-2185
-
(2003)
J. Math. Phys.
, vol.44
, pp. 2179-2185
-
-
Lenzi, E.K.1
Mendes, R.S.2
Fa, K.S.3
Malacarne, L.C.4
-
26
-
-
1542425102
-
Numerical solution of the space fractional Fokker-Planck equation
-
Liu F., Anh V., and Turner I. Numerical solution of the space fractional Fokker-Planck equation. J. Comput. Appl. Math. 166 (2004) 209-219
-
(2004)
J. Comput. Appl. Math.
, vol.166
, pp. 209-219
-
-
Liu, F.1
Anh, V.2
Turner, I.3
-
27
-
-
84966227123
-
Fractional linear multistep methods for Abel-Volterra integral equations of the second kind
-
Lubich C. Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Math. Comp. 45 (1985) 463-469
-
(1985)
Math. Comp.
, vol.45
, pp. 463-469
-
-
Lubich, C.1
-
28
-
-
0000717432
-
Discretized fractional calculus
-
Lubich C. Discretized fractional calculus. SIAM J. Math. Anal. 17 (1986) 704-719
-
(1986)
SIAM J. Math. Anal.
, vol.17
, pp. 704-719
-
-
Lubich, C.1
-
29
-
-
84926570205
-
Some noises with 1/f spectrum, a bridge between direct current and white noise
-
Mandelbrot B. Some noises with 1/f spectrum, a bridge between direct current and white noise. IEEE Trans. Inform. Theory 13 (1967) 289-298
-
(1967)
IEEE Trans. Inform. Theory
, vol.13
, pp. 289-298
-
-
Mandelbrot, B.1
-
30
-
-
25444463578
-
Finite difference methods for two-dimensional fractional dispersion equation
-
Meerschaert M.M., Scheffler H.-P., and Tadjeran C. Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 211 (2006) 249-261
-
(2006)
J. Comput. Phys.
, vol.211
, pp. 249-261
-
-
Meerschaert, M.M.1
Scheffler, H.-P.2
Tadjeran, C.3
-
31
-
-
18144408075
-
Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach
-
Metzler R., Barkai E., and Klafter J. Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach. Phys. Rev. Lett. 82 (1999) 3563
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 3563
-
-
Metzler, R.1
Barkai, E.2
Klafter, J.3
-
32
-
-
0002641421
-
The random walk's guide to anomalous diffusion: A fractional dynamics approach
-
see also references therein
-
Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1-77 see also references therein
-
(2000)
Phys. Rep.
, vol.339
, pp. 1-77
-
-
Metzler, R.1
Klafter, J.2
-
35
-
-
0001553919
-
Fractional diffusion and wave equations
-
Schneider W.R., and Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989) 134-144
-
(1989)
J. Math. Phys.
, vol.30
, pp. 134-144
-
-
Schneider, W.R.1
Wyss, W.2
-
36
-
-
0001691616
-
Observations of anomalous diffusion and Levy flights in a 2-dimensional rotating flow
-
Solomon T.H., Weeks E.R., and Swinney H.L. Observations of anomalous diffusion and Levy flights in a 2-dimensional rotating flow. Phys. Rev. Lett. 71 (1993) 3975-3979
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 3975-3979
-
-
Solomon, T.H.1
Weeks, E.R.2
Swinney, H.L.3
-
37
-
-
0026135818
-
Burgers equation with a fractional derivative: hereditary effects on nonlinear acoustic waves
-
Sugimoto N. 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
-
38
-
-
0036887936
-
Chaos, fractional kinetics, and anomalous transport
-
Zaslavsky G.M. Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371 (2002) 461-580
-
(2002)
Phys. Rep.
, vol.371
, pp. 461-580
-
-
Zaslavsky, G.M.1
|