环上Sobolev型的时间分数阶微分不等式

IF 1.9 3区 数学 Q1 MATHEMATICS, APPLIED
Axioms Pub Date : 2023-10-20 DOI:10.3390/axioms12100993
Amal Alshabanat, Eman Almoalim, Mohamed Jleli, Bessem Samet
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引用次数: 0

摘要

自然科学中的一些现象可以用sobolev型偏微分方程来描述。另一方面,研究表明,在许多情况下,使用分数阶导数比使用标准阶导数提供了一个更现实的模型。本文的目的是研究一类sobolev型时间分数阶微分不等式弱解的不存在性。也就是说,我们给出不存在的充分条件或存在的等价必要条件。我们的方法利用了非线性容量法,即在问题的弱形式中适当地选择测试函数。这一方法已在前人的研究中用于求解若干类全空间RN上的sobolev型时间分数阶微分不等式。这项工作的独创性在于所考虑的问题是在环域上提出的,这导致了一些关于选择适当的测试函数的困难。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Time-Fractional Differential Inequality of Sobolev Type on an Annulus
Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal of this paper is to study the nonexistence of weak solutions to a time-fractional differential inequality of Sobolev-type. Namely, we give sufficient conditions for the nonexistence or equivalently necessary conditions for the existence. Our method makes use of the nonlinear capacity method, which consists in making an appropriate choice of test functions in the weak formulation of the problem. This technique has been employed in previous papers for some classes of time-fractional differential inequalities of Sobolev-type posed on the whole space RN. The originality of this work is that the considered problem is posed on an annulus domain, which leads to some difficulties concerning the choice of adequate test functions.
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来源期刊
Axioms
Axioms Mathematics-Algebra and Number Theory
自引率
10.00%
发文量
604
审稿时长
11 weeks
期刊介绍: Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.
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