Basic results for fractional anisotropic spaces and applications

IF 0.9 3区 数学 Q2 MATHEMATICS
J. Vanterler da C. Sousa, Arhrrabi Elhoussain, El-Houari Hamza, Leandro S. Tavares
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引用次数: 0

Abstract

In this paper, we introduce a new space that generalizes the \(\phi \)-Hilfer space with the \(\xi (\cdot )\)-Laplacian operator, denoted \((\phi ,{\xi }(\cdot ))\)-HFDS. We refer to this new space as the \(\phi \)-fractional space with anisotropic \(\overrightarrow{\xi }(\cdot )\)-Laplacian operator, abbreviated as \((\phi ,\overrightarrow{\xi }(\cdot ))\)-HFDAS. We prove that \((\phi ,\overrightarrow{\xi }(\cdot ))\)-HFDAS is a separable, and reflexive Banach space. Furthermore, we extend some well-known properties and embedding results of the \((\phi ,\xi (\cdot ))\)-HFDS space to \((\phi ,\overrightarrow{\xi }(\cdot ))\)-HFDAS. Moreover, we illustrate an application of \((\phi ,\overrightarrow{\xi }(\cdot ))\)-HFDAS by solving a differential equation via variational methods.

分数各向异性空间的基本结果及其应用
在本文中,我们引入了一个新的空间,它概括了带有拉普拉卡算子的((\phi,{\xi }(\cdot ))\HFDS )的((\phi \)-Hilfer)空间。我们把这个新空间称为具有各向异性的(overrightarrow{xi }(\cdot ) )-拉普拉斯算子的(\phi \)-分形空间,简称为((\phi ,\overrightarrow{xi}(\cdot ) )-HFDAS。我们证明\((\phi ,\overrightarrow{xi }(\cdot ))\)-HFDAS 是一个可分离的、反身的巴拿赫空间。此外,我们将 \((\phi ,\xi (\cdot )))-HFDS空间的一些众所周知的性质和嵌入结果扩展到 \((\phi ,\overrightarrow{xi }(\cdot ))\)-HFDAS 中。此外,我们还通过变分法求解一个微分方程来说明了((\phi ,\overrightarrow\{xi}(\cdot ))\)-HFDAS 的应用。
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
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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