arXiv 1502.072772015-02-25math.CA

任意非空闭集上的非对称与对称分式演算

Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets

Nadia Benkhettou, Artur M. C. Brito da Cruz, Delfim F. M. Torres

备注：: This is a preprint of a paper whose final and definite form will be published in Mathematical Methods in the Applied Sciences, ISSN 0170-4214. Submitted 05/March/2014; revised 24/Feb/2015; accepted 25/Feb/2015. arXiv admin note: text overlap with arXiv:1405.2813
发表信息：: Math. Methods Appl. Sci. 39 (2016), no. 2, 261--279
DOI：: 10.1002/mma.3475

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摘要：

我们介绍了一个纳布拉，一个三角洲，和对称分数演算的任意非空闭子集的实数。这些分数阶微积分提供了一个研究微分和积分的非整数阶离散，连续和混合设置。研究了新的分数阶算子的主要性质，给出了一些基本结果，说明了离散和连续行为之间的相互作用。

英文摘要：

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of noninteger order on discrete, continuous, and hybrid settings. Main properties of the new fractional operators are investigated, and some fundamental results presented, illustrating the interplay between discrete and continuous behaviors.

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