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Nonlinear Dynamics

, Volume 74, Issue 1–2, pp 381–394 | Cite as

Non-standard fractional Lagrangians

  • Rami Ahmad El-Nabulsi
Original Paper

Abstract

Two mathematical physics’ approaches have recently gained increasing importance both in mathematical and in physical theories: (i) the fractional action-like variational approach which founds its significance in dissipative and non-conservative systems and (ii) the theory of non-standard Lagrangians which exist in some group of dissipative dynamical systems and are entitled “non-natural” by Arnold. Both approaches are discussed independently in the literature; nevertheless, we believe that the combination of both theories will help identifying more hidden solutions in certain classes of dynamical systems. Accordingly, we generalize the fractional action-like variational approach for the case of non-standard power-law Lagrangians of the form L 1+γ \((\gamma\in\mathbb{R})\) recently introduced by the author (Qual. Theory Dyn. Syst. doi: 10.1007/s12346-012-0074-0, 2012). Many interesting features are discussed in some details.

Keywords

Fractional non-standard Lagrangians Nonlinear dynamics 

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceNeijiang Normal UniversityNeijiangChina

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