Homogeneous Finsler spaces with some special (α, β)-metrics

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In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series (α, β)-metric and exponential metric. Next, we deduce an explicit formula for the the S-curvature of homogeneous Finsler space with these metrics. Using this formula, we further derive the formula for mean Berwald curvature of the homogeneous Finsler space with the above mentioned metrics.