Fractional integral approach to parameterized inequalities for (s,P)-preinvexity

Fractional calculus is an invaluable tool with significant potential for application in the physical sciences.This paper focuses on addressing parameterized fractional inequalities for (s,P) -preinvex functions.In light of this, we introduce the concept of (s,P) -preinvex functions and investigate their related properties.By considering limited first-and second-order derivative functions, we present two fractional integral identities with a single parameter using exponential kernel fractional integrals.Building upon these identities, we establish parameterized integral inequalities for (s,P) -preinvex functions.To provide a more intuitive display of the results, we also offer illustrative examples with graphs to demonstrate the validity of our theoretical findings.