Surveys in Mathematics and its Applications
ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 21 (2026), 9 -- 59
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This work is licensed under a Creative Commons Attribution 4.0 International License.

A COMPREHENSIVE STUDY ON OSTROWSKI-TYPE INEQUALITIES: MULTIPLICATIVE CONFORMABLE FRACTIONAL INTEGRALS APPROACH

Büşra Betül Ergün and Hüseyin Budak

Abstract. In this paper, we first recall the concept o f the multiplicative conformable fractional integrals (MCFI) and their several properties. Then, we establish the Ostrowski type inequalities in two distinct senses for multiplicative conformable fractional integrals. The reason for considering two distinct types of Ostrowski-type inequalities is to capture a broader class of functions and provide more general results that can be applied in different settings within the framework of multiplicative conformable fractional calculus For this aim we first prove two new equalities for multiplicative differentiable functions. Then, by advantage of these identities, we prove some Ostrowski-type inequalities by using the concept of multiplicative convex functions and the well-known Hölder inequality. Moreover, we establish Ostrowski type inequalities for functions whose multiplicative derivatives are bounded. By special cases, we present the relations between newly obtained inequalities for MCFI and existing results for multiplicative Riemann-Liouville fractional integrals (MRLFI) and multiplicative integrals. Furthermore, we give some new Ostrowski type inequalities for multiplicative integrals and MRLFI. Finally, we give several examples and 3D graphs to illustrate the main results.

2020 Mathematics Subject Classification: 26D10; 26A51; 26D15.
Keywords: Multiplicative calculus; Ostrowski inequality; Conformable fractional integrals

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Büşra Betül Ergün, ORCID: 0009-0009-4038-4487
Department of Mathematics, Faculty of Sciences and Art,
Kocaeli University, Kocaeli 41001, Türkiye.
e-mail: ergnbra12@gmail.com

Hüseyin Budak, ORCID: 0000-0001-8843-955X
1. Department of Mathematics, Faculty of Sciences and Art,
Kocaeli University, Kocaeli 41001, Türkiye.
2. Department of Mathematics, Saveetha School of Engineering,
SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India.
e-mail: hsyn.budak@gmail.com



Received: January 18, 2026; Accepted: March 10, 2026;
Published electronically: March 13, 2026.