Convex analysis and mathematical inequalities are now essential to the development of numerous pure and applied scientific domains. In this article, first we introduce the concept of n-fractional polynomial s-like m-preinvex function. In addition, we introduce, the new variant of Hermite-Hadamard type inequality via newly introduced concept pertaining to the k-fractional operator. Furthermore, we demonstrate the applications to matrix and bivariat analysis via newly introduce Hermite-Hadamard type inequality. The study’s conclusions present unique perspectives and contributions to the field, offering fresh and noteworthy improvements over previous research.