Damping characteristics of a fractional oscillator

Physica A: Statistical Mechanics and its Applications

Volumn 339, Issue 3-4, 2004, Pages 311-319

  Achar, B N Narahari ^a   Hanneken, John W ^a   Clarke, T ^a  

^a UNIVERSITY OF MEMPHIS   (United States)

Author keywords

Dynamic damping; Fractional calculus; Fractional oscillator

Indexed keywords

DAMPING; EQUATIONS OF MOTION; GREEN'S FUNCTION; HARMONIC ANALYSIS; MATHEMATICAL TECHNIQUES; NATURAL FREQUENCIES; PERTURBATION TECHNIQUES;

DYNAMIC DAMPING; FRACTIONAL CALCULUS; FRACTIONAL OSCILLATOR (FO); POWER-LAW TAIL;

OSCILLATORS (MECHANICAL);

EID: 2942532686     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.03.030     Document Type: Article

References (16)

1. Narahari Achar B.N., Hanneken J.W., Enck T., Clarke T. Physica A. 297:2001;361-367.
2. Gorenflo R., Mainardi F. Fractional calculus: integral and differential equations of fractional order. Carpinteri A., Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics. 1997;Springer, Wien, R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, preprint No. A-14/96, Fachbereich Mathematik und Informatik, Freie Universitat Berlin, (1996), http://www.math.fu-berlin.de/publ/index.html ; R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, International Workshop on the Recent Advances in Applied Mathematics (RAAM96), State of Kuwait, May 4-7, 1996, Proceedings, Kuwait University, 1996, pp. 193-208.
3. Gorenflo R., Mainardi F. Fractional calculus: integral and differential equations of fractional order. Carpinteri A., Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics. 1997;Springer, Wien, R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, preprint No. A-14/96, Fachbereich Mathematik und Informatik, Freie Universitat Berlin, (1996), http://www.math.fu-berlin.de/publ/index.html ; R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, International Workshop on the Recent Advances in Applied Mathematics (RAAM96), State of Kuwait, May 4-7, 1996, Proceedings, Kuwait University, 1996, pp. 193-208.
4. Gorenflo R., Mainardi F. Fractional calculus: integral and differential equations of fractional order. Carpinteri A., Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics. 1997;Springer, Wien, R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, preprint No. A-14/96, Fachbereich Mathematik und Informatik, Freie Universitat Berlin, (1996), http://www.math.fu-berlin.de/publ/index.html ; R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, International Workshop on the Recent Advances in Applied Mathematics (RAAM96), State of Kuwait, May 4-7, 1996, Proceedings, Kuwait University, 1996, pp. 193-208.
5. Gorenflo R., Rutman R. On ultraslow and on intermediate processes. Rusev P., Dimovski I., Kiryakova V. Transform Methods and Special Functions, Sophia, 1994. 1995;Science Culture and Technology, Singapore.
6. Mainardi F. Chaos, Solitons and Fractals. 7(9):1996;1461-1477.
7. Narahari Achar B.N., W. Hanneken John, Clarke T. Physica A. 309:2002;275-288.
8. Oldham K.B., Spanier J. The Fractional Calculus. 1974;Academic Press, New York.
9. Miller K., Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations. 1993;Wiley, New York.
10. Podlubny I. Fractional Differential Equations. 1999;Academic Press, San Diego.
11. Samko S.G., Kilbas A.A., Marichev O.I. Fractional Integrals and Derivatives: Theory and Applications. 1993;Gordon and Breach, Amsterdam.
12. Tofighi Ali Physica A. 329:2003;29-34.
13. Ryabov Ya.E., Puzenko A. Phys. Rev. B. 66:2002;184201-184208.
14. A. Erdélyi, Higher Transcendental Functions, Vol. III, McGraw-Hill, New York, 1955.
15. Gorenflo R., Loutchko J., Luchko Y. Fractional Calculus Appl. Anal. 5:2002;491-518.
16. Marion J.B., Thornton S.T. Classical Dynamics of Particles and Systems. 4th Edition:1995;Saunders, Fort Worth.