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Hybrid Fractional Integral Inequalities In Multiplicative Calculus With Applications

Author

Listed:
  • MUHAMMAD UMAR

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan)

  • SAAD IHSAN BUTT

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan)

  • YOUNGSOO SEOL

    (Department of Mathematics, Dong-A University, Busan 49315, Korea)

Abstract

Aspects of both hybrid and fractional calculus are combined in the (Proportional Caputo-Hybrid) Pcap operators, which are helpful in solving differential equations with non-integer orders and modeling a variety of complicated phenomena in science and engineering. In this paper, we establish the Pcap operators via multiplicative calculus which are termed as multiplicative Pcap operators. we initially formulate two H.H (Hermite–Hadamard)-type inequalities applicable to multiplicative (geometric) convex function via multiplicative Pcap operators. Subsequently, by leveraging certain characteristics of multiplicative convex functions, we present novel inequalities related to multiplicative convex function via multiplicative Pcap operators also demonstrating two novel identities applicable to multiplicatively differentiable functions. By leveraging these identities, we then establish inequalities of trapezoid and midpoint types specifically designed for multiplicatively convex functions. Additionally, we explore applications of these findings to special functions and special means.

Suggested Citation

  • Muhammad Umar & Saad Ihsan Butt & Youngsoo Seol, 2025. "Hybrid Fractional Integral Inequalities In Multiplicative Calculus With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-28.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:01:n:s0218348x25500197
    DOI: 10.1142/S0218348X25500197
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