2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137913Using the reviewed Riemann-Liouville fractional derivative 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.20 pages, the paper was presented at International Conference on Differential Geometry Lagrange and Hamilton Spaces, Dedicated to Acad. Radu Miron at eighty, September 3-8, 2007, Iasi, RomaniaDifferential Geometry26A33, 53C63, 58A05, 58A40text