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Volume 30, Issue 3
Fractional Variational Approach for Dissipative Mechanical Systems

R. A. El-Nabulsi

DOI: 10.4208/ata.2014.v30.n3.1

Anal. Theory Appl., 30 (2014), pp. 249-259.

Published online: 2014-10

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  • Abstract

More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their formalism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restrictions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.

  • Keywords

Fractional actionlike variational approach, dissipative system.

  • AMS Subject Headings

26A33, 49S05, 70F40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-30-249, author = {R. A. El-Nabulsi}, title = {Fractional Variational Approach for Dissipative Mechanical Systems}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {3}, pages = {249--259}, abstract = {

More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their formalism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restrictions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.1}, url = {http://global-sci.org/intro/article_detail/ata/4489.html} }
TY - JOUR T1 - Fractional Variational Approach for Dissipative Mechanical Systems AU - R. A. El-Nabulsi JO - Analysis in Theory and Applications VL - 3 SP - 249 EP - 259 PY - 2014 DA - 2014/10 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n3.1 UR - https://global-sci.org/intro/article_detail/ata/4489.html KW - Fractional actionlike variational approach, dissipative system. AB -

More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their formalism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restrictions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.

R. A. El-Nabulsi. (2014). Fractional Variational Approach for Dissipative Mechanical Systems. Analysis in Theory and Applications. 30 (3). 249-259. doi:10.4208/ata.2014.v30.n3.1
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