A generalization of HH f-divergence

The discrimination between two probability distributions is an impotent problem. In 1991, Lin [IEEE Transactions on Information Theory, 37(1) 1991] introduced a novel class of information-theoretic divergence measures based on the Shannon entropy. As a generalization of Lin's divergence, a new divergence, called Hermite-Hadamard (HH) f-divergence, based on Lin's method of constructing the divergence was introduced by Shioya and Da-te in 1995. In this paper, we expand the applicability of HH f-divergence by combining the properties of fractional calculus with HH f-divergence, and then introduce the concept of some fractional HH f-divergences which are generalizations of the HH f-divergence. Then, some inequalities related to fractional HH f-divergence are proposed.