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

Advances in Difference Equations

Antonio Coronel-Escamilla²  Ricardo Fabricio Escobar-Jimnez⁵  Dumitru Baleanu⁶  Jos Francisco Gmez-Aguilar⁷  Arturo Abundez-Pliego⁸  Victor Hugo Olivares-Peregrino⁹ 

[1] CONACYT - Centro Nacional de InvestigacióCentro Nacional de InvestigacióDepartment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Ankara, Turkey;Institute of Space Sciences, Magurele-Bucharest, Romania;gico Nacional de Mégico, Tecnolón y Desarrollo Tecnolóxico;xico, Cuernavaca, Mé

关键词: Pais-Uhlenbeck oscillator;    two-electric pendulum;    Caputo-Fabrizio operator;    Atangana-Baleanu-Caputo operator;    Crank-Nicholson scheme;    Euler-Lagrange formalism;   

DOI  :  10.1186/s13662-016-1001-5

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY