Raising the regularity of generalized Abel equations in fractional Sobolev spaces with homogeneous boundary conditions

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Integral Equations and Applications Pub Date : 2020-06-12 DOI:10.1216/jie.2021.33.327

Yulong Li

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引用次数: 3

Abstract

The generalized (or coupled) Abel equations on the bounded interval have been well investigated in H$\ddot{\text{o}}$lderian spaces that admit integrable singularities at the endpoints and relatively inadequate in other functional spaces. In recent years, such operators have appeared in BVPs of fractional-order differential equations such as fractional diffusion equations that are usually studied in the frame of fractional Sobolev spaces for weak solution and numerical approximation; and their analysis plays the key role during the process of converting weak solutions to the true solutions. This article develops the mapping properties of generalized Abel operators $\alpha {_aD_x^{-s}}+\beta {_xD_b^{-s}}$ in fractional Sobolev spaces, where $0<\alpha,\beta$, $\alpha+\beta=1$, $ 0

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齐次边界条件下分数阶Sobolev空间中广义Abel方程正则性的提高

有界区间上的广义（或耦合）Abel方程在H$\ddot｛\text｛o｝｝$lderian空间中得到了很好的研究，该空间允许在端点处存在可积奇点，而在其他函数空间中则相对不足。近年来，这类算子出现在分数阶微分方程的边值问题中，例如通常在分数阶Sobolev空间框架下研究的分数阶扩散方程，用于弱解和数值逼近；它们的分析在将弱解转化为真解的过程中起着关键作用。本文发展了分数阶Sobolev空间中广义Abel算子$\alpha｛_aD_x^｛-s｝｝+\beta｛_xD_b^｛-s｝｝$的映射性质，其中$0<\alpha，\beta$，$\alpha+\beta=1$，$0

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

Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.

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