-
1
-
-
0001926804
-
From dynamical systems to the langevin equation
-
[1] Beck, C., Roepstorff, G., From dynamical systems to the langevin equation. Phys A 145 (1987), 1–14.
-
(1987)
Phys A
, vol.145
, pp. 1-14
-
-
Beck, C.1
Roepstorff, G.2
-
2
-
-
0004217794
-
-
second ed. World Scientific Singapore
-
[2] Coffey, W.T., Kalmykov, Y.P., Waldron, J.T., The langevin equation, second ed., 2004, World Scientific, Singapore.
-
(2004)
The langevin equation
-
-
Coffey, W.T.1
Kalmykov, Y.P.2
Waldron, J.T.3
-
3
-
-
84889299911
-
-
Wiley-VCH Weinheim
-
[3] Klages, R., Radons, G., Sokolov, I.M., Anomalous transport: fundations and applications, 2008, Wiley-VCH, Weinheim.
-
(2008)
Anomalous transport: fundations and applications
-
-
Klages, R.1
Radons, G.2
Sokolov, I.M.3
-
4
-
-
33847327575
-
The fluctuation–dissipation theorem
-
[4] Kubo, R., The fluctuation–dissipation theorem. Rep Prog Phys 29 (1966), 255–284.
-
(1966)
Rep Prog Phys
, vol.29
, pp. 255-284
-
-
Kubo, R.1
-
5
-
-
0004138120
-
-
second ed. Springer–Verlag Berlin
-
[5] Kubo, R., Toda, M., Hashitsume, N., Statistical physics II, second ed., 1991, Springer–Verlag, Berlin.
-
(1991)
Statistical physics II
-
-
Kubo, R.1
Toda, M.2
Hashitsume, N.3
-
6
-
-
77951086281
-
Fractional generalized langevin equation approach to single–file diffusion
-
[6] Eab, C.H., Lim, S.C., Fractional generalized langevin equation approach to single–file diffusion. Phys A 389 (2010), 2510–2521.
-
(2010)
Phys A
, vol.389
, pp. 2510-2521
-
-
Eab, C.H.1
Lim, S.C.2
-
7
-
-
84887894098
-
Langevin equation for a free particle driven by power law type of noises
-
[7] Sandev, T., Tomovski, Z., Langevin equation for a free particle driven by power law type of noises. Phys Lett A 378 (2014), 1–9.
-
(2014)
Phys Lett A
, vol.378
, pp. 1-9
-
-
Sandev, T.1
Tomovski, Z.2
-
8
-
-
84865117591
-
Langevin equation with multiplicative white noise: transformation of diffusion processes into the wiener process in different prescriptions
-
[8] Kwok, S.F., Langevin equation with multiplicative white noise: transformation of diffusion processes into the wiener process in different prescriptions. Ann Phys 327 (2012), 1989–1997.
-
(2012)
Ann Phys
, vol.327
, pp. 1989-1997
-
-
Kwok, S.F.1
-
9
-
-
84923280073
-
Ulam–hyers stability of fractional langevin equations
-
[9] Wang, J.R., Li, X., Ulam–hyers stability of fractional langevin equations. Appl Math Comput 258 (2015), 72–83.
-
(2015)
Appl Math Comput
, vol.258
, pp. 72-83
-
-
Wang, J.R.1
Li, X.2
-
10
-
-
76449113714
-
Fractional diffusion equations by the kansa method
-
[10] Chen, W., Ye, L., Sun, H., Fractional diffusion equations by the kansa method. Comput Math Appl 59 (2010), 1614–1620.
-
(2010)
Comput Math Appl
, vol.59
, pp. 1614-1620
-
-
Chen, W.1
Ye, L.2
Sun, H.3
-
11
-
-
84930374284
-
Method of approximate particular solutions for constant–and variable–order fractional diffusion models
-
[11] Fu, Z.J., Chen, W., Ling, L., Method of approximate particular solutions for constant–and variable–order fractional diffusion models. Eng Anal Bound Elem 57 (2015), 37–46.
-
(2015)
Eng Anal Bound Elem
, vol.57
, pp. 37-46
-
-
Fu, Z.J.1
Chen, W.2
Ling, L.3
-
12
-
-
84871003930
-
Boundary particle method for laplace transformed time fractional diffusion equations
-
[12] Fu, Z.J., Chen, W., Yang, H.T., Boundary particle method for laplace transformed time fractional diffusion equations. J Comput Phys 235 (2013), 52–66.
-
(2013)
J Comput Phys
, vol.235
, pp. 52-66
-
-
Fu, Z.J.1
Chen, W.2
Yang, H.T.3
-
13
-
-
84890797227
-
Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders
-
[13] Yu, T., Deng, K., Luo, M., Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders. Commun Nonlinear Sci Numer Simulat 19 (2014), 1661–1668.
-
(2014)
Commun Nonlinear Sci Numer Simulat
, vol.19
, pp. 1661-1668
-
-
Yu, T.1
Deng, K.2
Luo, M.3
-
14
-
-
52349118652
-
Langevin equation with two fractional orders
-
[14] Lim, S.C., Li, M., Teo, L.P., Langevin equation with two fractional orders. Phys Lett A 372 (2008), 6309–6320.
-
(2008)
Phys Lett A
, vol.372
, pp. 6309-6320
-
-
Lim, S.C.1
Li, M.2
Teo, L.P.3
-
15
-
-
64549125064
-
The fractional oscillator process with two indices
-
[15] Lim, S.C., Teo, L.P., The fractional oscillator process with two indices. J Phys A, 42, 2009, 065208.
-
(2009)
J Phys A
, vol.42
, pp. 065208
-
-
Lim, S.C.1
Teo, L.P.2
-
16
-
-
77956906008
-
Solvability of nonlinear langevin equation involving two fractional orders with dirichlet boundary conditions
-
[16] Ahmad, B., Nieto, J.J., Solvability of nonlinear langevin equation involving two fractional orders with dirichlet boundary conditions. Int J Differ Equ, 2010, 1649486.
-
(2010)
Int J Differ Equ
, pp. 1649486
-
-
Ahmad, B.1
Nieto, J.J.2
-
17
-
-
80054946851
-
A study of nonlinear langevin equation involving two fractional orders in different intervals
-
[17] Ahmad, B., Nieto, J.J., Alsaedi, A., El-Shahed, M., A study of nonlinear langevin equation involving two fractional orders in different intervals. Nonlinear Anal RWA 13 (2012), 599–606.
-
(2012)
Nonlinear Anal RWA
, vol.13
, pp. 599-606
-
-
Ahmad, B.1
Nieto, J.J.2
Alsaedi, A.3
El-Shahed, M.4
-
18
-
-
77049084247
-
Initial value problems for fractional differential equations involving riemann–liouville sequential fractional derivative
-
[18] Wei, Z., Li, Q., Chea, J., Initial value problems for fractional differential equations involving riemann–liouville sequential fractional derivative. J Math Anal Appl 367 (2010), 260–272.
-
(2010)
J Math Anal Appl
, vol.367
, pp. 260-272
-
-
Wei, Z.1
Li, Q.2
Chea, J.3
-
19
-
-
59849083895
-
Integral equations and initial value problems for nonlinear differential equations of fractional order
-
[19] Kosmatov, N., Integral equations and initial value problems for nonlinear differential equations of fractional order. Nonlinear Anal 70 (2009), 2521–2529.
-
(2009)
Nonlinear Anal
, vol.70
, pp. 2521-2529
-
-
Kosmatov, N.1
-
20
-
-
77950188013
-
Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
-
[20] Deng, J., Ma, L., Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. Appl Math Lett 23 (2010), 676–680.
-
(2010)
Appl Math Lett
, vol.23
, pp. 676-680
-
-
Deng, J.1
Ma, L.2
-
21
-
-
84896765881
-
Existence of solutions of initial value problems for nonlinear fractional differential equations
-
[21] Deng, J., Deng, Z., Existence of solutions of initial value problems for nonlinear fractional differential equations. Appl Math Lett 32 (2014), 6–12.
-
(2014)
Appl Math Lett
, vol.32
, pp. 6-12
-
-
Deng, J.1
Deng, Z.2
-
22
-
-
77949264980
-
A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
-
[22] Agarwal, R.P., Benchohra, M., Hamani, S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl Math 109 (2010), 973–1033.
-
(2010)
Acta Appl Math
, vol.109
, pp. 973-1033
-
-
Agarwal, R.P.1
Benchohra, M.2
Hamani, S.3
-
23
-
-
80053385595
-
Existence of solutions for fractional differential equations with multi–point boundary conditions
-
[23] Zhou, W.X., Chu, Y.D., Existence of solutions for fractional differential equations with multi–point boundary conditions. Commun Nonlinear Sci Numer Simulat 17 (2012), 1142–1148.
-
(2012)
Commun Nonlinear Sci Numer Simulat
, vol.17
, pp. 1142-1148
-
-
Zhou, W.X.1
Chu, Y.D.2
-
24
-
-
51349139941
-
Theory of fractional functional differential equations
-
[24] Lakshmikantham, V., Theory of fractional functional differential equations. Nonlinear Anal 69 (2008), 3337–3343.
-
(2008)
Nonlinear Anal
, vol.69
, pp. 3337-3343
-
-
Lakshmikantham, V.1
-
25
-
-
53949111458
-
Basic theory of fractional differential equations
-
[25] Lakshmikantham, V., Vatsala, A.S., Basic theory of fractional differential equations. Nonlinear Anal 69 (2008), 2677–2682.
-
(2008)
Nonlinear Anal
, vol.69
, pp. 2677-2682
-
-
Lakshmikantham, V.1
Vatsala, A.S.2
-
26
-
-
45049084850
-
General uniqueness and monotone iterative technique for fractional differential equations
-
[26] Lakshmikantham, V., Vatsala, A.S., General uniqueness and monotone iterative technique for fractional differential equations. Appl Math Lett 21 (2008), 828–834.
-
(2008)
Appl Math Lett
, vol.21
, pp. 828-834
-
-
Lakshmikantham, V.1
Vatsala, A.S.2
-
27
-
-
77950019962
-
Existence and uniqueness of solutions to singular ODEs
-
[27] Gorka, P., Rybka, P., Existence and uniqueness of solutions to singular ODEs. Arch Math 94 (2010), 227–233.
-
(2010)
Arch Math
, vol.94
, pp. 227-233
-
-
Gorka, P.1
Rybka, P.2
-
28
-
-
44049117892
-
Weakly lipschitzian mappings and restricted uniqueness of solutions of ordinary differential equations
-
[28] Owen, D.R., Wang, K., Weakly lipschitzian mappings and restricted uniqueness of solutions of ordinary differential equations. J Differ Equ 95 (1992), 385–398.
-
(1992)
J Differ Equ
, vol.95
, pp. 385-398
-
-
Owen, D.R.1
Wang, K.2
-
29
-
-
0343368357
-
The fractional langevin equation: brownian motion revisited
-
[29] Mainardi, F., Pironi, P., The fractional langevin equation: brownian motion revisited. Extracta math 11 (1996), 140–154.
-
(1996)
Extracta math
, vol.11
, pp. 140-154
-
-
Mainardi, F.1
Pironi, P.2
-
31
-
-
34247154280
-
Global existence theory and chaos control of fractional differential equations
-
[31] Lin, W., Global existence theory and chaos control of fractional differential equations. J Math Anal Appl 332 (2007), 709–726.
-
(2007)
J Math Anal Appl
, vol.332
, pp. 709-726
-
-
Lin, W.1
-
32
-
-
33847309315
-
-
Elsevier Amsterdam
-
[32] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, 2006, Elsevier, Amsterdam.
-
(2006)
Theory and applications of fractional differential equations
-
-
Kilbas, A.A.1
Srivastava, H.M.2
Trujillo, J.J.3
-
34
-
-
0021439912
-
On the appearance of the fractional derivative in the behavior of real materials
-
[34] Bagly, R.L., Torvik, P.J., On the appearance of the fractional derivative in the behavior of real materials. J Appl Mech 51 (1984), 294–298.
-
(1984)
J Appl Mech
, vol.51
, pp. 294-298
-
-
Bagly, R.L.1
Torvik, P.J.2
|