The fractional oscillator as an open system

[1] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives Theory and Applications, (Gordon and Breach, New York, 1993) Search in Google Scholar

[2] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations, (Elsevier, Amsterdam, 2006) Search in Google Scholar

[3] I. Podlubny, Fractional Differential Equations, (Academic Press, San Diego, 1999) Search in Google Scholar

[4] G.M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, Oxford, 2005) Search in Google Scholar

[5] B. West, M. Bologna, P. Grigolini, Physics of Fractal Operators (Springer, New York, 2003) 10.1007/978-0-387-21746-8Search in Google Scholar

[6] A. Carpinteri, F. Mainardi, (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, (Springer, Wien, 1997) 10.1007/978-3-7091-2664-6Search in Google Scholar

[7] R. Hilfer, (Ed.), Applications of Fractional Calculus in Physics, (World Scientific, Singapore, 2000) 10.1142/3779Search in Google Scholar

[8] J. Sabatier, O.P. Agrawal, J.A. Tenreiro Machado, (Eds.), Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering, (Springer, Dordrecht, 2007) 10.1007/978-1-4020-6042-7Search in Google Scholar

[9] V.V. Uchaikin, Method of Fractional Derivatives, (Artishok, Ulyanovsk, 2008) in Russian. Search in Google Scholar

[10] A.C.J. Luo, V.S. Afraimovich (Eds.), Long-range Interaction, Stochasticity and Fractional Dynamics, (Springer, Berlin, 2010) 10.1007/978-3-642-12343-6Search in Google Scholar

[11] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, (World Scientific, Singapore, 2010) http://dx.doi.org/10.1142/978184816330010.1142/p614Search in Google Scholar

[12] V.E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, (Springer, New York, 2010) 10.1007/978-3-642-14003-7_11Search in Google Scholar

[13] J. Klafter, S.C. Lim, R. Metzler (Eds.), Fractional Dynamics. Recent Advances, (World Scientific, Singapore, 2011) 10.1142/8087Search in Google Scholar

[14] V.E. Tarasov, Theoretical Physics Models with Integro-Differentiation of Fractional Order, (IKI, RCD, 2011) in Russian Search in Google Scholar

[15] V.E. Tarasov, G.M. Zaslavsky, Chaos 16, 023110 (2006) http://dx.doi.org/10.1063/1.219716710.1063/1.2197167Search in Google Scholar PubMed

[16] V.E. Tarasov, G.M. Zaslavsky, Commun. Nonlin. Sci. Numer. Simul. 11, 885 (2006) http://dx.doi.org/10.1016/j.cnsns.2006.03.00510.1016/j.cnsns.2006.03.005Search in Google Scholar

[17] N. Laskin, G.M. Zaslavsky, Physica A 368, 38 (2006) http://dx.doi.org/10.1016/j.physa.2006.02.02710.1016/j.physa.2006.02.027Search in Google Scholar

[18] N. Korabel, G.M. Zaslavsky, V.E. Tarasov, Commun. Nonlin. Sci. Numer. Simul. 12, 1405 (2007) http://dx.doi.org/10.1016/j.cnsns.2006.03.01510.1016/j.cnsns.2006.03.015Search in Google Scholar

[19] V.E. Tarasov, J. Math. Phys. 47, 092901 (2006) http://dx.doi.org/10.1063/1.233785210.1063/1.2337852Search in Google Scholar

[20] W. Min, G. Luo, B.J. Cherayil, S.C. Kou, X.S. Xie, Phys. Rev. Lett. 94, 198302 (2005) http://dx.doi.org/10.1103/PhysRevLett.94.19830210.1103/PhysRevLett.94.198302Search in Google Scholar PubMed

[21] H. Mori, Prog. Theor. Phys. 33, 423 (1965) http://dx.doi.org/10.1143/PTP.33.42310.1143/PTP.33.423Search in Google Scholar

[22] R. Kubo, Rep. Prog. Phys. 29, 255 (1966) http://dx.doi.org/10.1088/0034-4885/29/1/30610.1088/0034-4885/29/1/306Search in Google Scholar

[23] S. Kempfle, I. Schafer, H. Beyer, Nonlinear Dynam. 29, 99 (2002) http://dx.doi.org/10.1023/A:101659510747110.1023/A:1016595107471Search in Google Scholar

[24] F. Mainardi, in W.F. Ames (Ed.), Proceedings 12-th IMACS World Congress, Vol. 1, 329 (1994) Search in Google Scholar

[25] F. Mainardi, P. Pironi, Extracta Mathematicae 10, 140 (1996) Search in Google Scholar

[26] V. Kobelev, E. Romanov, Prog. Theor Phys Suppl. 139, 470 (2000) http://dx.doi.org/10.1143/PTPS.139.47010.1143/PTPS.139.470Search in Google Scholar

[27] E. Lutz, Phys. Rev. E 64, 051106 (2001) http://dx.doi.org/10.1103/PhysRevE.64.05110610.1103/PhysRevE.64.051106Search in Google Scholar PubMed

[28] A. A. Stanislavsky, Phys. Rev. E 67, 021111 (2003) http://dx.doi.org/10.1103/PhysRevE.67.02111110.1103/PhysRevE.67.021111Search in Google Scholar PubMed

[29] K. S. Fa, Phys. Rev. E 73, 061104 (2006) http://dx.doi.org/10.1103/PhysRevE.73.06110410.1103/PhysRevE.73.061104Search in Google Scholar

[30] K. S. Fa, Eur. Phys. J. E 24, 139 (2007) http://dx.doi.org/10.1140/epje/i2007-10224-210.1140/epje/i2007-10224-2Search in Google Scholar

[31] S. Burov, E. Barkai, Phys. Rev. Lett. 100, 070601 (2008) http://dx.doi.org/10.1103/PhysRevLett.100.07060110.1103/PhysRevLett.100.070601Search in Google Scholar

[32] S. Burov, E. Barkai, Phys. Rev. E 78, 031112 (2008) http://dx.doi.org/10.1103/PhysRevE.78.03111210.1103/PhysRevE.78.031112Search in Google Scholar

[33] S.C. Lima, M. Lib, L.P. Teoc, Phys. Lett. A 372, 6309 (2008) http://dx.doi.org/10.1016/j.physleta.2008.08.04510.1016/j.physleta.2008.08.045Search in Google Scholar

[34] R.F. Camargo, A.O. Chiacchio, R. Charnet, E.C. Oliveira, J. Math. Phys. 50, 06350 (2009) 10.1063/1.3152608Search in Google Scholar

[35] R. Gorenflo, F. Mainardi, In: Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi (Ed.), (Springer, Wien and New York 1997) 223 10.1007/978-3-7091-2664-6_5Search in Google Scholar

[36] F. Mainardi, R. Gorenflo, J. Comput. Appl. Math. 118, 283 (2000) http://dx.doi.org/10.1016/S0377-0427(00)00294-610.1016/S0377-0427(00)00294-6Search in Google Scholar

[37] F. Mainardi, Chaos Solitons Fractals, 7, 1461 (1996) http://dx.doi.org/10.1016/0960-0779(95)00125-510.1016/0960-0779(95)00125-5Search in Google Scholar

[38] G. M. Zaslavsky, A.A. Stanislavsky, M. Edelman, Chaos 16, 013102 (2006) http://dx.doi.org/10.1063/1.212680610.1063/1.2126806Search in Google Scholar PubMed

[39] A.A. Stanislavsky, Phys. Rev. E 70, 051103 (2004) http://dx.doi.org/10.1103/PhysRevE.70.05110310.1103/PhysRevE.70.051103Search in Google Scholar

[40] A.A. Stanislavsky, Physica A 354, 101, (2005) http://dx.doi.org/10.1016/j.physa.2005.02.03310.1016/j.physa.2005.02.033Search in Google Scholar

[41] A.A. Stanislavsky, Eur. Phys. J. B, 49, 93 (2006) http://dx.doi.org/10.1140/epjb/e2006-00023-310.1140/epjb/e2006-00023-3Search in Google Scholar

[42] V.E. Tarasov, G.M. Zaslavsky, Physica A 368, 399 (2006) http://dx.doi.org/10.1016/j.physa.2005.12.01510.1016/j.physa.2005.12.015Search in Google Scholar

[43] B.N.N. Achar, J.W. Hanneken, T. Clarke, Physica A 339, 311 (2004) http://dx.doi.org/10.1016/j.physa.2004.03.03010.1016/j.physa.2004.03.030Search in Google Scholar

[44] B.N.N. Achar, J.W. Hanneken, T. Clarke, Physica A 309, 275 (2002) http://dx.doi.org/10.1016/S0378-4371(02)00609-X10.1016/S0378-4371(02)00609-XSearch in Google Scholar

[45] B.N.N. Achar, J.W. Hanneken, T. Enck, T. Clarke, Physica A 297, 361 (2001) http://dx.doi.org/10.1016/S0378-4371(01)00200-X10.1016/S0378-4371(01)00200-XSearch in Google Scholar

[46] A. Tofighi, Physica A 329, 29 (2003) http://dx.doi.org/10.1016/S0378-4371(03)00598-310.1016/S0378-4371(03)00598-3Search in Google Scholar

[47] A. Tofighi, H.N. Poura, Physica A 374, 41 (2007) http://dx.doi.org/10.1016/j.physa.2006.07.02510.1016/j.physa.2006.07.025Search in Google Scholar

[48] V.E. Tarasov, Phys. Lett. A. 372, 2984 (2008) http://dx.doi.org/10.1016/j.physleta.2008.01.03710.1016/j.physleta.2008.01.037Search in Google Scholar

[49] V.E. Tarasov, Theor. Math. Phys. 158, 179 (2009) http://dx.doi.org/10.1007/s11232-009-0015-510.1007/s11232-009-0015-5Search in Google Scholar

[50] V.E. Tarasov, J. Math. Phys. 49, 102112 (2008) http://dx.doi.org/10.1063/1.300953310.1063/1.3009533Search in Google Scholar

[51] V.E. Tarasov, In: Fractional Dynamics in Physics: Recent Advances, J. Klafter, S.C. Lim, R. Metzler (Eds.), Chapter 19 (World Scientific, Singapore, 2011) 447 Search in Google Scholar

[52] F. Riewe, Phys. Rev. E 55, 3581 (1997) http://dx.doi.org/10.1103/PhysRevE.55.358110.1103/PhysRevE.55.3581Search in Google Scholar

[53] O.P. Agrawal, J. Math. Anal. 272, 368 (2002) http://dx.doi.org/10.1016/S0022-247X(02)00180-410.1016/S0022-247X(02)00180-4Search in Google Scholar

[54] M. Klimek, Czech. J. Phys. 51, 1348 (2001) http://dx.doi.org/10.1023/A:101337822161710.1023/A:1013378221617Search in Google Scholar

[55] V.E. Tarasov, G.M. Zaslavsky, J. Phys. A. 39, 9797 (2006) http://dx.doi.org/10.1088/0305-4470/39/31/01010.1088/0305-4470/39/31/010Search in Google Scholar

[56] D. Baleanu, J. Comput. Nonlin. Dyn. 3, 021102 (2008) http://dx.doi.org/10.1115/1.283358610.1115/1.2833586Search in Google Scholar

[57] D. Baleanu J.I. Trujillo, Commun. Nonlinear. Sci. 15, 1111 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.05.02310.1016/j.cnsns.2009.05.023Search in Google Scholar

[58] D. Baleanu, A.K. Golmankhaneh, A.K. Golmankhaneh, R.R. Nigmatullin, Nonlin. Dyn. 60, 81 (2010) http://dx.doi.org/10.1007/s11071-009-9581-110.1007/s11071-009-9581-1Search in Google Scholar

[59] D. Baleanu, A.K. Golmankhaneh, R.R. Nigmatullin, A.K. Golmankhaneh, Cent. Eur. J. Phys. 8, 120 (2010) http://dx.doi.org/10.2478/s11534-009-0085-x10.2478/s11534-009-0085-xSearch in Google Scholar

[60] A.K. Golmankhaneh, A.K. Golmankhaneh, D. Baleanu, M.C. Baleanu, Adv. Differ. Equ. 2011, 526472 (2011) 10.1155/2011/526472Search in Google Scholar

[61] Y.E. Ryabov, A. Puzenko, Phys. Rev. B 66, 184201 (2002) http://dx.doi.org/10.1103/PhysRevB.66.18420110.1103/PhysRevB.66.184201Search in Google Scholar

[62] H. Bateman, A. Erdelyi, Tables of Integral Transform, Vol. 1. (McGraw-Hill, New York, 1954) Search in Google Scholar

[63] M. Abramowitz, I.A. Stegun, (Eds.), in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Sec. 5.2, 9th printing, 231 (Dover, New York, 1972) Search in Google Scholar

[64] O.P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002) http://dx.doi.org/10.1016/S0022-247X(02)00180-410.1016/S0022-247X(02)00180-4Search in Google Scholar

[65] O.P. Agrawal, J. Phys. A. 40, 6287 (2007) http://dx.doi.org/10.1088/1751-8113/40/24/00310.1088/1751-8113/40/24/003Search in Google Scholar

[66] R. Gorenflo, J. Loutchko, Y. Luchko, Fract. Calc. Appl. Anal. 5, 491 (2002) Search in Google Scholar

[67] L. Accardi, Y.G. Lu, I.V. Volovich, Quantum Theory and Its Stochastic Limit, (Springer Verlag, New York, 2002) 10.1007/978-3-662-04929-7Search in Google Scholar

[68] S. Attal, A. Joye, C.A. Pillet, (Eds.), Open Quantum Systems: The Markovian Approach, (Springer, 2006) 10.1007/b128451Search in Google Scholar

[69] E.B. Davies, Quantum Theory of Open Systems, (Academic Press, London, 1976) Search in Google Scholar

[70] R.S. Ingarden, A. Kossakowski, M. Ohya, Information Dynamics and Open Systems: Classical and Quantum Approach, (Kluwer, New York, 1997) 10.1007/978-94-017-1882-0Search in Google Scholar

[71] V.E. Tarasov, Quantum Mechanics of Non-Hamiltonian and Dissipative Systems, (Elsevier, Amsterdam, Boston, London, New York, 2008) Search in Google Scholar

[72] H.P. Breuer, F. Petruccione, Theory of Open Quantum Systems, (Oxford University Press, 2002) Search in Google Scholar