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Formulation of Euler-Lagrange and Hamilton equations involving fractional operators with regular kernel

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Abstract

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 gamma.

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Olivares Peregrino, Victor Hugo/0000-0002-5214-4984; Escobar Jimenez, Ricardo Fabricio/0000-0003-3367-6552; Coronel-Escamilla, Antonio/0000-0003-3662-2939; Abundez-Pliego, Arturo/0000-0001-8220-4338; Gomez-Aguilar, J.F./0000-0001-9403-3767

Keywords

Pais-Uhlenbeck Oscillator, Two-Electric Pendulum, Caputo-Fabrizio Operator, Atangana-Baleanu-Caputo Operator, Crank-Nicholson Scheme, Euler-Lagrange Formalism

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Baleanu, D...[et.al.]. (2016). Formulation of Euler-Lagrange and Hamilton equations involving fractional operators with regular kernel. Advances In Difference Equations. http://dx.doi.org/10.1186/s13662-016-1001-5

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