this paper, we us the Hermite-Hadamard inequality and the Riemann-Liouville fractional integral operator to obtain an inequality to generalize that generalize known results on the Tsallis relative operator entropy; the elementary convex power function is used in a fundamental way. Using our adopted inequality, we generalize the notion of the Tsallis relative operator entropy to the fractional case. This allows us to extend previous bounds on the fractional Tsallis relative operator entropy.

Keywords: Fractional integral, Relative operator entropy, Tsallis relative operator entropy, Hermite-Hadamard&rsquo,s inequality