Journal
NONLINEAR DYNAMICS
Volume 74, Issue 1-2, Pages 381-394Publisher
SPRINGER
DOI: 10.1007/s11071-013-0977-6
Keywords
Fractional non-standard Lagrangians; Nonlinear dynamics
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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+gamma) 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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