In this paper, we give new versions of Hermite–Hadamard inequality via pseudo-fractional integral of order a > 0 in two classes of semiring ð½a; b; ; Þ: We show that if pseudo operations are defined by an increasing and continuous function g, then we can replace the convexity of g with a weaker condition. Also, for the second semiring ð½a; b; sup; Þ; we propose a new version of Hermite–Hadamard inequality, where the pseudo-multiplication is generated by g. An example to illustrate results is given.
