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August 2, 2026Fractals

On the Theory of Multiplicative Conformable Fractional Integrals and Their Applications to Hermite-Hadamard and Maclaurin-Type Inequalities

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New multiplicative conformable fractional integrals establish inequalities in positive functions, suggesting broader applications.

This research aims to introduce and explore multiplicative conformable fractional integrals within the framework of non-Newtonian calculus.
Defined multiplicative conformable integrals and constructed multiplicative conformable fractional integrals.
Investigated fundamental properties of the newly defined integrals.
Established associated multiplicative Hermite-Hadamard and Maclaurin-type inequalities.
Demonstrated that the constructed multiplicative conformable fractional integrals maintain significant flexibility in modeling.
Derived inequalities that reflect the relationships of these integrals based on [Formula: see text]-convexity.
Showed potential applications of these inequalities in scaling and exponential models.

Lakhdari et al. (2026) studied this question.

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