Boundary Value Problem for a Degenerate Equation of Even Order With a Fractional Derivative in a Mixed Domain

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-31 DOI:10.1002/mma.70012

B. Yu. Irgashev

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引用次数: 0

Abstract

In this paper, in a rectangular domain, we study a Dirichlet-type problem with gluing conditions for a degenerate high-order equation with fractional derivatives in the Riemann–Liouville sense of orders $α \in (1, 2)$ , for $y > 0$ , and $β \in (1, 2)$ , for $y < 0$ . A criterion for the uniqueness of the solution of the stated problem is given. Using asymptotic expansions for the Mittag–Leffler function and Bessel's inequality, sufficient conditions for the existence of a solution are found.

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混合域上具有分数阶导数的偶阶退化方程的边值问题

本文在矩形域上，研究了一类退化高阶分数阶方程在α∈(1,2)$$ \alpha \in \left(1,2\right) $$的Riemann-Liouville意义下的带胶合条件的dirichlet型问题。对于y ＆gt； 0 $$ y>0 $$, β∈(1,2)$$ \beta \in \left(1,2\right) $$，对于y ＆lt； 0 $$ y<0 $$。给出了该问题解的唯一性判据。利用Mittag-Leffler函数和Bessel不等式的渐近展开式，得到了解存在的充分条件。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.