Abstract In this article, we introduce the concept of α-fractionally convex functions. We primarily focus on characterizing some of the qualitative properties of convex functions with the assistance of fractional order operators. Also, we discuss the connection of optimality, monotonicity, and convexity of a function in the sense of fractional calculus. Several examples are provided to support the proposed formulation, and one can establish the fractional convexity of a non-convex function.

中文翻译：

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α-分数凸函数

摘要 在本文中，我们介绍了α-分数凸函数的概念。我们主要关注在分数阶算子的帮助下表征凸函数的一些定性特性。此外，我们还讨论了分数阶微积分意义上的函数的最优性、单调性和凸性之间的联系。提供了几个示例来支持所提出的公式，并且可以建立非凸函数的分数凸性。