The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

本文讨论了分形集上p-凸函数的概念。我们能够证明一个新颖的辅助结果。在应用方面，局部分数的保真度用于为在某些幂处的绝对分数的局部分数导数是p-凸的函数的函数类建立Simpson型不等式的推广。我们展示的方法是显示与广义p相关的经典变体的替代方法-凸函数。我们的结果的某些部分涵盖了经典凸函数和经典谐波凸函数。获得了一些在随机变量，累积分布函数和广义双变量均值上的新颖应用，以确保当前结果的正确性。本方法是有效，可靠的，并且可以用作为计算机图形学中不同类型的分形建立新解决方案的替代方法。