A new weighted fractional operator with respect to another function via a new modified generalized Mittag–Leffler law

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-06 DOI:10.1186/s13661-023-01790-7

Sabri T. M. Thabet, Thabet Abdeljawad, Imed Kedim, M. Iadh Ayari

引用次数: 0

Abstract

Abstract In this paper, new generalized weighted fractional derivatives with respect to another function are derived in the sense of Caputo and Riemann–Liouville involving a new modified version of a generalized Mittag–Leffler function with three parameters, as well as their corresponding fractional integrals. In addition, several new and existing operators of nonsingular kernels are obtained as special cases of our operator. Many important properties related to our new operator are introduced, such as a series version involving Riemann–Liouville fractional integrals, weighted Laplace transforms with respect to another function, etc. Finally, an example is given to illustrate the effectiveness of the new results.

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利用一个新的改进的广义Mittag-Leffler定律，得到一个关于另一个函数的新的加权分数算子

摘要本文在Caputo和Riemann-Liouville意义下，导出了关于另一函数的新的广义加权分数阶导数，涉及到具有三个参数的广义Mittag-Leffler函数的一个新的修正版本，以及相应的分数阶积分。此外，作为该算子的特例，还得到了一些新的和已有的非奇异核算子。介绍了与我们的新算子相关的许多重要性质，如涉及Riemann-Liouville分数积分的级数版本，关于另一个函数的加权拉普拉斯变换等。最后，通过一个算例说明了新结果的有效性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.