This paper deals with the computation of the two parameter Mittag-Leffler function of operators by exploiting its Stieltjes integral representation and then by using a single exponential transform together with the sinc rule. Whenever the parameters of the function do not allow this representation, we resort to the Dunford-Taylor one. The error analysis is kept in the framework of unbounded accretive operators in order to make it a useful tool for the solution of fractional differential equations. The theory is also used to design a rational Krylov method.

中文翻译：

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关于增加算子分数幂的 Mittag-Leffler 函数的计算

本文通过利用运算符的 Stieltjes 积分表示，然后将单个指数变换与 sinc 规则一起使用，来处理运算符的双参数 Mittag-Leffler 函数的计算。每当函数的参数不允许这种表示时，我们就会求助于 Dunford-Taylor 的表示。误差分析保存在无界累积算子的框架中，以使其成为求解分数阶微分方程的有用工具。该理论还用于设计有理的 Krylov 方法。