Fractional Euler-Lagrange Equations of Order（alpha,beta）for Lie Algebroids

Abstract

The main purpose of this paper is to derive the fractional Euler-Lagrange equations which depend on the Riemann-Liouville derivatives of order for Lie algebroids. The fractional Hamiltonian formalism was also discussed. Two examples in particular the fractional geodesics for Lie algebroids and the Wong's fractional equations which arise in the dynamics of a colored particle in Yang-Mills field and on the falling cat theorem were also derived. Key Words: Fractional Action-like Variational Approach; Fractional Lagrangian and Hamiltonian Formalisms; Lie Algebroids