  In this paper, a new notion, named Riemann-Liouville fractional cosine
function is presented. It is proved that a Riemann-Liouville $\alpha$-order
fractional cosine function is equivalent to Riemann-Liouville $\alpha$-order
fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math.
Nachr. 288, No. 7, 784-797 (2015)].
