A comprehensive survey on recent advances in multiplicative fractional calculus and related integral inequalities

The present article intends to give a comprehensive survey of recent developments in the literature on multiplicative fractional integral inequalities. In contrast to Newton and Leibnitz calculus, multiplicative calculus has a comparatively narrower range of applications. In actuality, it exclusively addresses positive functions. Multiplicative calculus is a valuable mathematical tool for several scientific fields, such as finance and economics, as it allows for multiple interpretations of the logarithmic scale through multiplicative derivatives. Fractional calculus, or the mathematical method of differentiation and integration of arbitrary order, has begun to get scientific attention due to its importance in numerous domains, including signal processing, physics, engineering, biology, and mechanics. This work seeks to draw researchers’ attention to multiplicative fractional calculus, which integrates concepts from both multiplicative and fractional calculus. It reviews representative recent contributions related to multiplicative fractional integral inequalities and outlines possible directions for future research.