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  • 标题:Formulation of Euler-Lagrange and Hamilton equations involving fractional operators with regular kernel
  • 本地全文:下载
  • 作者:Antonio Coronel-Escamilla ; José Francisco Gómez-Aguilar ; Dumitru Baleanu
  • 期刊名称:Advances in Difference Equations
  • 印刷版ISSN:1687-1839
  • 电子版ISSN:1687-1847
  • 出版年度:2016
  • 卷号:2016
  • 期号:1
  • 页码:283
  • DOI:10.1186/s13662-016-1001-5
  • 语种:English
  • 出版社:Hindawi Publishing Corporation
  • 摘要:This paper presents alternative representations to traditional calculus of the Euler-Lagrangian equations, in the alternative representations these equations contain fractional operators. In this work, we consider two problems, the Lagrangian of a Pais-Uhlenbeck oscillator and the Hamiltonian of a two-electric pendulum model where the fractional operators have a regular kernel. The Euler-Lagrange formalism was used to obtain the dynamic model based on the Caputo-Fabrizio operator and the new fractional operator based on the Mittag-Leffler function. The simulations showed the effectiveness of these two representations for different values of γ.
  • 关键词:Pais-Uhlenbeck oscillator ; two-electric pendulum ; Caputo-Fabrizio operator ; Atangana-Baleanu-Caputo operator ; Crank-Nicholson scheme ; Euler-Lagrange formalism
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