量子微积分中带有Sturm-Liouville算子的热波方程

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2023-01-19 DOI:10.1155/2023/2488165

S. Shaimardan, L. Persson, N. Tokmagambetov

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引用次数: 0

摘要

在本文中，我们探索了由Jackson算子和q-Sturm-Liouville算子分别关于t和x生成的q-热方程和q-波方程的Cauchy问题的广义解。为此，我们使用了一种新方法，其中使用了一个关键工具来表示量子微积分中希尔伯特空间中傅立叶级数展开中的函数。我们证明了这些解可以用q-Mittag-Leffler函数生成的显式公式来表示。此外，我们还证明了弱解的唯一存在性和稳定性。

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On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus

In this paper, we explore a generalised solution of the Cauchy problems for the q -heat and q -wave equations which are generated by Jackson’s and the q -Sturm-Liouville operators with respect to t and x , respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions can be represented by explicit formulas generated by the q -Mittag-Leffler function. Moreover, we prove the unique existence and stability of the weak solutions.

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.