We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional integral operator which has many interesting properties. The motivation for these definitions is twofold: firstly, their link with some fundamental fractional differential equations involving two independent fractional orders, and secondly, the fact that they emerge naturally from certain applications in bioengineering.

中文翻译：

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自然出现的二元Mittag-Leffler函数和相关的分数微积分算子

我们定义了适用于两个变量的经典Mittag-Leffler函数的类似物，并建立了其基本属性。使用具有分数幂的相应单变量函数，我们定义了一个关联的分数积分算子，该算子具有许多有趣的属性。这些定义的动机是双重的：首先，它们与涉及两个独立分数阶的基本分数阶微分方程的联系；其次，它们从生物工程中的某些应用中自然产生的事实。