New Variant of Hermite–Hadamard, Fejér and Pachpatte-Type Inequality and Its Refinements Pertaining to Fractional Integral Operator

In order to show novel generalizations of mathematical inequality, fractional integral operators are frequently used. Fractional used simulate a broad range scientific as well engineering phenomena such elasticity, viscous fluid, fracture mechanics, continuous population, equilibrium, visco-elastic deformation, heat conduction problems, and others. this manuscript, we introduce some notions generalized preinvexity, namely the (m,tgs)-type s-preinvex function, Godunova–Levin (s,m)-preinvex 1st 2nd kind, prequasi m-invex. Furthermore, explore new variant Hermite–Hadamard (H–H), Fejér, Pachpatte-type inequality via operator, namely, non-conformable operator (NCFIO). addition, equalities. With help these equalities, examine present several extensions H–H Fejér-type inequalities involving newly introduced concept NCFIO. Finally, special means applications in aspects The results unique situations offered by research significant improvements over previously published findings.