Browsing by Author "Dr. SAAD IHSAN BUTT"

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    New Harmonic Multiplicative Fractional Integral Inequalities
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Noor-ul-Ain; CIIT/SP24-RMT-015/LHR; Dr. SAAD IHSAN BUTT; LHR TP 10076
    In this work, we consider the concept of strongly multiplicatively harmonic convex function (SMHCf ). We establish integral inequalities of Hermite-Hadamard (HH) type inequalities for the product and quotient results, in the frame of multiplicative calculus. We discuss the characteristics of SMHCf function. Further, we derive inequalities of trapezoid and mid- point type. In addition, we also verify the validity of our results by graphical descriptions. Also, we enhance our research by offering various applications to specialfunctions.
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    New Multiplicative Fractional Integral Inequalities
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Zain Ali; CIIT/SP24-RMT-018/LHR; Dr. SAAD IHSAN BUTT; LHR TP 10079
    In the context of multiplicative fractional calculus, we develop new Hermite-Hadamard (HH) type inequalities and present the concept of multiplicative trigonometric exponen- tial convex (MTEC) functions. We investigate their algebraic properties and show how these functions relate to other types of convex functions. Several new fractional HH type inequalities are constructed by employing product and quotient of newly introduced multi- plicative convexities via multiplicative Riemann-Liouville (RL) integrals operator. Further, we derive some fractional auxiliary results of trapezoid and midpoint type and apply our convexities to formulate new bounds. In addition, we also verify the validity of our results by graphical descriptions. We also strengthen our study by providing some applications to special functions.