Coronel-Escamilla, AntonioFrancisco Gomez-Aguilar, JoseBaleanu, DumitruFabricio Escobar-Jimenez, RicardoHugo Olivares-Peregrino, VictorAbundez-Pliego, ArturoMatematik2018-09-272018-09-272016Baleanu, 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/s13662-016-1001-51687-1847https://doi.org/10.1186/s13662-016-1001-5Olivares 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./0000-0001-9403-3767This 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.eninfo:eu-repo/semantics/openAccessPais-Uhlenbeck OscillatorTwo-Electric PendulumCaputo-Fabrizio OperatorAtangana-Baleanu-Caputo OperatorCrank-Nicholson SchemeEuler-Lagrange FormalismArticle10.1186/s13662-016-1001-52-s2.0-85013879094WOS:000387547400001Q1N/A