Generalized fractional operators for nonstandard Lagrangians

Generalized fractional operators for nonstandard Lagrangians

In this note, we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems, and the corresponding Euler–Lagrange and Hamilton equations are analyzed. The dependence of the equation of motion on the generalized...

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Veröffentlicht in:Mathematical methods in the applied sciences 2015-06, Vol.38 (9), p.1808-1812
Hauptverfasser: Taverna, Giorgio S., Torres, Delfim F.M.
Format: Artikel
Sprache:eng
Schlagworte:
Dissipation
dissipative systems
Equations of motion
Euler-Lagrange and Hamilton equations
generalized fractional calculus of variations
generalized fractional operators
Kernels
Mathematical analysis
nonstandard Lagrangians
Operators
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Zusammenfassung:In this note, we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems, and the corresponding Euler–Lagrange and Hamilton equations are analyzed. The dependence of the equation of motion on the generalized kernel permits to obtain a wide range of different configurations of motion. Some examples are discussed and analyzed.Copyright © 2014 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3188