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Non-standard fractional Lagrangians

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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.

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  1. College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan, 641112, China

    Rami Ahmad El-Nabulsi

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El-Nabulsi, R.A. Non-standard fractional Lagrangians. Nonlinear Dyn 74, 381–394 (2013). https://doi.org/10.1007/s11071-013-0977-6

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