CHINESE ANNALS OF MATHEMATICS SERIES B, cilt.42, sa.1, ss.41-68, 2021 (SCI-Expanded)
Considering the prolongation of a Lie algebroid, the authors introduce Finsler algebroids and present important geometric objects on these spaces. Important endomorphisms like conservative and Barthel, Cartan tensor and some distinguished connections like Berwald, Cartan, Chern-Rund and Hashiguchi are introduced and studied.