A Novel Fractional Integral of a Function via Polynomial $n$-Fractional $s$-Like Preinvexity

In the following numerical novel, we develop a new fractional integral operator that incorporates polynomials \(n\)-fractional with \(s\)-like preinvexity, thus expanding the notion of fractional calculus. This new operator provides a more comprehensive framework for examining the behavior of functions exhibiting generalized preinvexity properties which are crucial in many optimization problems. We investigate the existence, uniqueness, and stability of this fractional integral as well as its basic characteristics. In addition, we provide a number of inequalities that show how useful this operator is in the context of applied sciences and mathematical analysis. Our results not only advance the theory of fractional calculus but also pave the way for future investigations into integral inequalities and fractional optimization.