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In this article, we develop a novel framework to study a new class of convex functions known as  n -polynomial    $\mathscr{P} $  P -convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by using a generalized  k -fractional Hilfer–Katugampola derivative. We employ this technique by using the Hölder and power-mean integral inequalities. We present analogs of the Ostrowski-type integrals inequalities connected with the  n -polynomial    $\mathscr{P}$  P -convex function. Some new exceptional cases from the main results are obtained, and some known results are recaptured. In the end, an application to special means is given as well. The article seeks to create an exciting combination of a convex function and special functions in fractional calculus. It is supposed that this investigation will provide new directions in fractional calculus.

Ostrowski-type inequalities for n-polynomial $\mathscr{P}$-convex function for k-fractional Hilfer–Katugampola derivative