Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

CiteULike is a free service for managing and discovering scholarly references - click here to get started.

Sign In to gain access to subscriptions and/or personal tools.
Journal of Vibration and Control
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Baleanu, D.
Right arrow Articles by Muslih, S. I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Nonconservative Systems within Fractional Generalized Derivatives

Dumitru Baleanu

Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Çankaya University, Balgat 06530, Ankara, Turkey, Institute of Space Sciences, P.O.BOX, MG-23, 76900, Magurele-Bucharest, Romania, dumitru{at}cankaya.edu.tr, baleanu{at}venus.nipne.ro

Sami I. Muslih

Department of Physics, Al-Azhar University, Gaza, International Center for Theoretical Physics (ICTP), Trieste, Italy

A fractional derivative generalizes an ordinary derivative, and therefore the derivative of the product of two functions differs from that for the classical (integer) case; the integration by parts for Riemann-Liouville fractional derivatives involves both the left and right fractional derivatives. Despite these restrictions, fractional calculus models are good candidates for description of nonconservative systems. In this article, nonconservative Lagrangian mechanics are investigated within the fractional generalized derivative approach. The fractional Euler-Lagrange equations based on the Riemann-Liouville fractional derivatives are briefly presented. Using generalized fractional derivatives, we give a meaning for the term which appears in fractional Euler-Lagrange equations and contains the second order fractional derivative. The fractional Lagrangians and Hamiltonians of two illustrative nonconservative mechanical systems are investigated in detail.

Key Words: Nonconservative systems • fractional derivatives • generalized derivatives • fractional Lagrangian • fractional Hamiltonian • fractional Euler-Lagrange equations

Journal of Vibration and Control, Vol. 14, No. 9-10, 1301-1311 (2008)
DOI: 10.1177/1077546307087450
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?