Abstract Fractional differential equations have been studied due to their applications in modelling, and solved using various mathematical methods. Systems of fractional differential equations are also used, for example in the study of electric circuits, but they are more difficult to analyse mathematically. We present explicit solutions for several families of such systems, both homogeneous and inhomogeneous cases, both commensurate and incommensurate. The results can be written, in several interesting special cases, in terms of a recently defined bivariate Mittag-Leffler function and the associated operators of fractional calculus.

中文翻译：

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非公度分数阶微分方程组的显式解析解

摘要 分数阶微分方程因其在建模中的应用而被研究，并使用各种数学方法求解。分数阶微分方程组也用于例如电路研究，但它们更难以数学分析。我们为此类系统的几个家族提供了明确的解决方案，包括同质和非同质情况，有相称的和不相称的。在几个有趣的特殊情况下，可以根据最近定义的二元 Mittag-Leffler 函数和分数阶微积分的相关运算符来编写结果。