A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems

The European Physical Journal Special Topics - Tập 193 Số 1 - Trang 185-192 - 2011
HongGuang Sun1, W. Chen1, Hui Wei1, YangQuan Chen2
1Institute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University, No.1 XiKang Road, Nanjing, Jiangsu 210098, China
2Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 4160 Old Main Hill, Logan, UT 84322-4160, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

S. Westerlund, Phys. Scripta 43, 174 (1991)

C.F.M. Coimbra, Ann. Phys. (Leipzig) 12, 692 (2003)

D. Ingman, J. Suzdalnitsky, M. Zeifman, J. Appl. Mech. 67, 383 (2000)

D. Ingman, J. Suzdalnitsky, J. Eng. Mech. 131, 763 (2005)

R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)

F. Mainardi, A. Mura, G. Pagnini, R. Gorenflo, J. Vib. Contr. 14, 1267 (2008)

H.G. Sun, W. Chen, Y.Q. Chen, Phys. A 388, 4586 (2009)

A.W. Lo, Econometrica 59, 1279 (1991)

S.Z. Rida, A.M.A. El-Sayed, A.A.M. Arafa, J. Stat. Phys. 140, 797 (2010)

B.J. West, E.L. Geneston, P. Grigolini, Phys. Rep. 468, 1 (2008)

C.P. Li, W.G. Sun, New Trends Nanotechnol. Fract. Calcul. Appl. 3, 243 (2010)

A.J. Turski, B. Atamaniuk, E. Turska, J. Tech. Phys. 44, 193 (2003)

R.L. Bagley, Torvik P.J., Int. J. Appl. Math. 2, 865 (2000)

I.M. Sokolov, A.V. Chechkin, J. Klafter, Acta Phys. Pol. B 35, 1323 (2004)

C.P. Li, W.H. Deng, Appl. Math. Comput. 187, 777 (2007)

I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)

C.A. Monje, Y.Q. Chen, B.M. Vinagre, D.Y. Xue, V. Feliu, Fractional-order Systems and Controls (Springer-Verlag, London, 2010)

F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticy (Imperial College Press, London, 2010)

E.N. de Azevedo, P.L. de Sousa, R.E. de Souza, M. Engelsberg, M. de N. do N. Miranda, M.A. Silva, Phys. Rev. E 73, 011204 (2006)

Y. He, S. Burov, R. Metzler, E. Barkai, Phys. Rev. Lett. 101, 058101 (2008)

K. Weron, M. Kotulski, Phys. A 232, 180 (1996)

S.G. Samko, B. Ross, Integral Trans. Spec. Funct. 1, 277 (1993)

S.G. Samko, J. Anal. Math. 21, 213 (1995)

A.V. Chechkin, R. Gorenflo, I.M. Sokolov, J. Phys. A: Math. Gen. 38, L679 (2005)

A.V. Chechkin, V. Yu. Gonchar, R. Gorenflo, N. Korabel, I.M. Sokolov, Phys. Rev. E 78, 021111 (2008)

Ya. L. Kobelev, L.Ya. Kobelev, Yu. L. Klimontovich, Dokl. Phys. 48, 285 (2003)

C.F. Lorenzo, T.T. Hartley, Nonlinear Dyn. 29, 57 (2002)

H.G. Sun, W. Chen, H. Sheng, Y.Q. Chen, Phys. Lett. A 374, 906 (2010)

B. Ross, S.K. Samko, Int. J. Math. Math. Sci. 18, 777 (1995)

C.M. Soon, C.F.M. Coimbra, M.H. Kobayashi, Ann. Phys. (Leipzig) 14, 378 (2005)

R. Metzler, J. Klafter, J. Non-Crystalline Solids 305, 81 (2002)

F. Mainardi, Chaos, Soliton & Fractal 7, 1461 (1996)

V.V. Anh, J.M. Angulo, M.D. Ruiz-Medina, Nonlinear Ana. 63, e2043 (2005)

J.D. Bao, Y.Z. Zhuo, Phys. Rev. Lett. 91, 138104 (2003)

N. Heymans, I. Podlubny, Rheol. Acta. 45, 765 (2006)

H.G. Sun, Y.Q. Chen, W. Chen, Signal Processing 91, 525 (2011)

K. Diethelm, N.J. Ford, A.D. Freed, Nonlinear Dyn. 29, 3 (2002)

T.A.M. Langlands, B.I. Henry, J. Comp. Phys. 205, 719 (2005)

H.G. Sun, Y.Q. Chen, W. Chen, 2010, http://www.mathworks.com/matlabcentral/fileexchange/26407

P. Zhuang, F. Liu, V. Anh, I. Turner, SIAM J. Numer. Anal. 47, 1760 (2009)

P. Zhuang, F. Liu, V. Anh, I. Turner, SIAM J. Numer. Anal. 47, 1760 (2009)