The geometry of fractional osculator bundle of higher order and applications

Abstract

Using the reviewed Riemann-Liouville fractional derivative we define the bundle Eak= Oscak(M) and highlight geometrical structures with a geometrical character. Also, we introduce the fractional osculator Lagrange space of k order and the main structures on it. The results are applied at the k order fractional prolongation of Lagrange, Finsler and Riemann fractional structures.