The purpose of this paper is to establish some refinements of Riemann--Liouville fractional Hermite--Hadamard inequalities for $(\alpha,m)$-logarithmically convex functions. By using our fractional integrals identities, we present some interesting and new left type fractional Hermite-Hadamard inequalities for once and twice differentiable $(\alpha,m)$-logarithmically convex functions via powerful series.