The definition and properties of the multiplicative derivative for the function $f: I^{\circ}\subseteq \mathbb{R}\to \mathbb{R^+}$ are given at the beginning of this abstract. Additionally, this paper gives a comprehensive description of the multiplicative integral and clarifies the characteristics that differentiate it from other types of integrals. In the realm of non-Newtonian calculus, the technique of multiplicative integration by parts is considered an important instrument. Secondly, this constitutes the first definition of $h$-convexity that is multiplicative by the use of the $B$-function, in addition to a number of cases in which convexity is multiplicative. This research provides evidence of a new form that utilizes the multiplicative absolute value, which is represented as $| \cdot |^{*}$, as well as other distinctive traits that have not been seen before. A presentation is offered that discusses the multiplicative Riemann–Liouville fractional integral operators of order $\alpha > 0$. These operators are formed based on a function $f : [a,b] \to \mathbb{R^{+}}$, where $\mathbb{R^{+}}$ represents the set of positive real numbers. This strategy framework proposes a new technique for dealing with the idea of multiplicative Weddle inequalities, and it is outlined in this publication. This is based on the ideas of fractional integrals as described by Riemann–Liouville. We put forward evidence that suggests the existence of yet another level of inequality. This conclusion is reached on the premise that the function in question is a multiplicative h-convex and that a multiplicative absolute value with unique properties exists. The findings that are provided are calculated by using multiplicatively $P$-functions in conjunction with multiplicatively $s$-convex functions.