In this paper, a strongly modified $(\alpha ,h-m)-p$-convex function, which is a class of strongly convex functions, was defined, and the properties of this function were proved. Initially, the Hermite-Hadamard type inequality was proved for the presented function class. Then, the Hermite-Hadamard type inequality was obtained for the $(k,r)$-Riemann-Liouville fractional integrals. Also, some examples were included. The results were generalizations of various results in the literature.