El-Nabulsi, Rami Ahmad Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent. (English) Zbl 1348.70076 Comput. Appl. Math. 33, No. 1, 163-179 (2014). Summary: Recently, the topics of fractional calculus of variations and non-standard Lagrangians have gained increasing importance both in mathematical and physical theories. In this paper, we generalize the fractional action-like variational approach characterized by a time-dependent fractional exponent for the case of non-standard Lagrangians. We show that many familiar oscillatory systems follow directly from this new approach. Some consequences are given accordingly. Cited in 22 Documents MSC: 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 26A33 Fractional derivatives and integrals 49S05 Variational principles of physics Keywords:fractional action-like variational approach; non-standard Lagrangians; time-dependent fractional exponent; fractional oscillators PDFBibTeX XMLCite \textit{R. A. El-Nabulsi}, Comput. Appl. Math. 33, No. 1, 163--179 (2014; Zbl 1348.70076) Full Text: DOI References: [1] Abramowitz M, Stequn IA (1965) Handbook of mathematical functions: with formulas, graphs and mathematical tables. Dover Publications, New York [2] Agrawal OP, Muslih SI, Baleanu D (2011) Generalized variational calculus in terms of multi-parameters fractional derivatives. Commun Nonlinear Sci Numer Simul 16:4756–4767 · Zbl 1236.49030 [3] Almeida R, Torres DFM (2009) Calculus of variations with fractional derivatives and fractional integrals. 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