The geometry of fractional tangent bundle and applications

Abstract

The authors present the use of the revised fractional Riemann-Liouville derivative in the fractional tangent bundle of order k, TM ak, of a differential manifold M and the behavior of some objects under a change of local map. Among the geometrical structures defined on Tak M we consider the fractional connections and the fractional Euler-Lagrange equations associated to a function defined Tak M. Some examples are given.