Hira Inamfa21-RMT-008Dr. saad urllah But2026-03-122022https://repository.cuilahore.edu.pk/handle/123456789/2707In this proposal, we will introduce some fractional auxiliary equalities in Mercer sense. By using these equalities, we will give fractional Trapezoid Mercer type inequalities. We will use concept of line of support to obtain new Mercer type inequalities. Thus, these refinements allow us to develop new extensions for integral inequalities. We will prove new Hermite-Hadamard (H-H) type inequalities with special functions involving fractional operators. For the development of these new integral inequalities, we will use H¨older and Power-mean integral inequalities. Visual illustrations demonstrate the accuracy and supremacy of the offered technique. We will reduce complicated integrals into simple forms by involving special functions. Hence, we will give new outcomes by using idea of earlier outcomes.en-USNew Fractional Extensions of Hadamard Mercer InequalitiesThesis