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The study of curvature properties of homogeneous Finsler spaces with$(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finslergeometry. In this paper, we consider homogeneous Finsler spaces with squaremetric and Randers change of square metric. First, we derive the explicitformulae for Ricci curvature of homogeneous Finsler spaces with these metrics.Next, we find a necessary and sufficient condition under which a homogeneousFinsler space with either of these metrics is of vanishing $S$-curvature. Theformulae for Ricci curvature of homogeneous Finsler spaces with square metricand Randers change of square metric having vanishing $S$-curvature areestablished. Finally, we prove that the aforesaid spaces having vanishing$S$-curvature and negative Ricci curvature must be Riemannian.

On the Ricci curvature of homogeneous Finsler spaces with $(\alpha,\beta)$-metrics