FRACTIONAL VERSION OF BULLEN-TYPE INEQUALITIES VIA MULTIPLICATIVE CALCULUS WITH APPLICATIONS

Saad Ihsan Butt (), Muhammad Umar (), Dawood Khan () and Youngsoo Seol
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Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Muhammad Umar: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Dawood Khan: Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
Youngsoo Seol: Department of Mathematics, Dong-A University, Busan 49315, Korea

FRACTALS (fractals), 2025, vol. 33, issue 09, 1-23

Abstract: Aspects of both hybrid and fractional calculus are combined in the proportional Caputo-hybrid (PCH) 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 PCH operators via multiplicative calculus which are termed as multiplicative PCH operators. We initially formulate Bullen-type (Bln-type) identity applicable to multiplicative (geometric) convex function via multiplicative PCH operators. Subsequently, leveraging certain characteristics of multiplicative convex functions, we present novel inequalities related to multiplicative convex functions via multiplicative PCH operators. Additionally, we explore applications of these findings to special functions and special means.

Keywords: Multiplicative Calculus; Multiplicative Convex Function; Hermite–Hadamard Inequality; Multiplicative Proportional Caputo-Hybrid Operator; Bessel Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500756

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