Complex Lie algebroids and Finsler manifold in time-dependent fractal dimension and their associated decomplexifications (Q2041096)

Fractional calculus is a generalisation of classical calculus, where fractional or fractal powers of differentiation and integration operators are considered. This paper is concerned with fractional calculus of variations for Lie algebroids and Finsler manifolds. The aim is to generalize previous studies to the case of fractional variational problems, i.e. fractional actions where the fractional order of the derivative is allowed to be time dependent. The basic fractional Lagrangian concepts and the fractional formalism on Finsler manifolds are introduced. Starting from such formalism, one could construct several geometric objects such as connections, torsions and parallel curvatures on prolongations of complex Lie algebroids.