In this paper, we propose a fresh conception about convexity, known as the multiplicative $(s,P)$-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the ${}^{\ast }$differentiable $(s,P)$-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well.

中文翻译：

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乘法微积分中的乘法 (s,P) 凸性和相关分数不等式

在本文中，我们提出了一个关于凸性的新概念，称为乘法$（s,磷）$-凸性。沿着这个方向，我们研究了此类凸性的性质。在乘法分数黎曼-刘维尔积分的框架下${}^{*}$可微的$（s,磷）$-凸性，我们研究乘法分数不等式，包括埃尔米特-哈达玛和牛顿型不等式。为了进一步验证我们主要结果的有效性，我们给出了一些数值例子。作为应用，我们还以特殊方式提供了许多乘法类型的不等式。