This paper discuses the decomposition of Fundamental Function of Finsler space by Lie-derivative in generalized fifth recurrent Finsler space for Cartan's fourth curvature tensor Kⱼkhⁱ in sense of Berwald. The decomposition of Lie-derivative of some tensors is studied by using a covariant, contravariant and mixed tensor in GBK-5RF_ (n). The decomposition tensor φₖhⁱbehaves as fifth-recurrent is proved. Also, new identities are established in generalized BK- fifth recurrent Finsler space that admits tensors decomposition.
Adel Alqashbri (2026) studied this question.