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June 2016 Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator
Rami Ahmad El-Nabulsi
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Tbilisi Math. J. 9(1): 279-293 (June 2016). DOI: 10.1515/tmj-2016-0014

Abstract

We extend the fractional actionlike variational approach where we substitute the standard Lagrangian by a non-standard power-law Lagrangian holding a generalized derivative operator. We focus on degenerate Lagrangians for the constructed fractional formalism where we show that non-linear oscillators with damping solutions may be obtained from degenerate non-standard Lagrangians which are linear in velocities. We explore as well the case of $2^{nd}$-order derivatives non-standard Lagrangians and we study the case where Lagrangians are linear in accelerations where damping solutions are obtained as well. It was observed that these extensions give another possibility to obtain more fundamental aspects which may have interesting classical effects.

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Rami Ahmad El-Nabulsi. "Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator." Tbilisi Math. J. 9 (1) 279 - 293, June 2016. https://doi.org/10.1515/tmj-2016-0014

Information

Received: 23 August 2015; Accepted: 25 March 2016; Published: June 2016
First available in Project Euclid: 12 June 2018

zbMATH: 1366.37128
MathSciNet: MR3528290
Digital Object Identifier: 10.1515/tmj-2016-0014

Subjects:
Primary: 37N05
Secondary: 49K10, 49K22

Rights: Copyright © 2016 Tbilisi Centre for Mathematical Sciences

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Vol.9 • No. 1 • June 2016
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