The sine and cosine diffusive representations for the Caputo fractional derivative

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-21 DOI:10.1016/j.apnum.2024.06.017

Hassan Khosravian-Arab , Mehdi Dehghan

引用次数: 0

Abstract

In recent years, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome the mentioned challenge. This paper presents two new diffusive representations to approximate the Caputo fractional derivative of order $0 < α < 1$ . An error analysis of the newly presented methods together with some numerical examples is provided at the end.

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卡普托分数导数的正弦和余弦扩散表示法

近年来，人们提出了各种类型的卡普托分数导数数值近似方法。这些方法面临的一个共同挑战是卡普托分数导数的非局部特性，这导致了这些方法速度慢、内存消耗大。分数导数的扩散表示是克服上述难题的有效工具。本文提出了两种新的扩散表示法来近似阶数为 0<α<1 的卡普托分数导数，并在最后提供了新方法的误差分析和一些数值示例。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.