Akademik Veri Yönetim Sistemi
Surveys in Mathematics and its Applications, cilt.21, ss.9-59, 2026 (Scopus)
In this paper, we first recall the concept of 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.