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A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators
Computational and Applied Mathematics ( IF 2.5 ) Pub Date : 2020-06-27 , DOI: 10.1007/s40314-020-01224-5 Arran Fernandez , Cemaliye Kürt , Mehmet Ali Özarslan
Computational and Applied Mathematics ( IF 2.5 ) Pub Date : 2020-06-27 , DOI: 10.1007/s40314-020-01224-5 Arran Fernandez , Cemaliye Kürt , Mehmet Ali Özarslan
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:
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。
更新日期:2020-06-27
中文翻译:
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。