  The theory of derivative of noninteger order goes back to Leibniz, Liouville
and Riemann. Derivatives of fractional order have found many applications in
recent studies in mechanics, physics, economics. In this paper we define the
fractional tangent bundle on a manifold, using a method of Radu Miron. The
fractional Leibniz algebroids are investigated. The associated objects have an
geometric character. Some fractional dynamical systems on a fractional Leibniz
algebroid are disscussed.
