Composition of Fractional Integral and Derivative Operators: Summarised in Tables

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-08-09 Epub Date: 2026-05-20 DOI:10.1002/mma.70794

Arran Fernandez

引用次数: 0

Abstract

This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption. The principle of analytic continuation for fractional differintegrals, generally underappreciated in the literature, helps to make the results more concise and natural. These results for Riemann–Liouville operators are well known classically, so here are also presented, for the first time, the corresponding results for the general transmuted operators, which include as special cases all fractional differintegrals taken with respect to monotonic functions, of both left-sided and right-sided types. For verifiability and self-containedness, full proofs are included, even for the classical results, as an appendix.

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分数阶积分和导数算子的组成：表中总结

本文编制了Riemann-Liouville分数阶微分积分的合成性质的完整、详细的列表，在所有可能的情况下，在复平面的任何地方的顺序，结果在一个表中清晰地呈现出来，以便于视觉消费。分数阶微分积分的解析延拓原理，通常在文献中被低估，有助于使结果更简洁和自然。Riemann-Liouville算子的这些结果在经典中是众所周知的，因此这里也首次给出了一般变换算子的相应结果，其中包括作为特殊情况的关于单调函数的所有分数阶微分积分，包括左型和右型。对于可验证性和自包含性，完整的证明包括，即使是经典的结果，作为附录。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.