On the computation of the Mittag-Leffler function of fractional powers of accretive operators

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-10-21 DOI:10.1007/s13540-024-00349-2

Eleonora Denich, Paolo Novati

引用次数: 0

Abstract

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.

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关于分数幂增量算子的米塔格-勒弗勒函数的计算

本文通过利用运算符的斯蒂尔杰斯积分表示法，然后使用单指数变换和 sinc 规则，来计算双参数米塔格-勒弗勒函数。每当函数参数不允许使用这种表示法时，我们就采用 Dunford-Taylor 表示法。误差分析保持在无界增量算子的框架内，以便使其成为求解分数微分方程的有用工具。该理论还用于设计一种有理克雷洛夫方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.