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The theory of derivative of noninteger order goes back to Leibniz, Liouvilleand Riemann. Derivatives of fractional order have found many applications inrecent studies in mechanics, physics, economics. In this paper we define thefractional tangent bundle on a manifold, using a method of Radu Miron. Thefractional Leibniz algebroids are investigated. The associated objects have angeometric character. Some fractional dynamical systems on a fractional Leibnizalgebroid are disscussed.

Fractional Dynamical Systems on Fractional Leibniz Algebroids