Properties of a Partial Fredholm Integro-differential Equations with Nonlocal Condition and Algorithms

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics Pub Date : 2024-08-06 DOI:10.1007/s00009-024-02712-2

Dulat S. Dzhumabaev, Anuar D. Dzhumabaev, Anar T. Assanova

引用次数: 0

Abstract

The paper is concerned with a nonlocal problem for a partial Fredholm integro-differential equation (IDE) of hyperbolic type is investigated. This problem is reduced to a problem containing a family of boundary value problems for the ordinary Fredholm IDEs and some integral relationships. A novel concept of general solution to a family of the ordinary Fredholm IDEs is introduced, and its properties are discussed. A necessary and sufficient condition for the well-posedness of the nonlocal problem for the partial Fredholm integro-differential equation (IDE) of hyperbolic type is obtained, and an algorithm for finding its solution is offered.

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具有非局部条件的部分弗雷德霍尔积分微分方程的性质与算法

本文研究的是一个双曲型偏弗雷德霍姆积分微分方程（IDE）的非局部问题。该问题被简化为一个包含普通弗雷德霍姆积分微分方程边界值问题族和一些积分关系的问题。引入了普通弗雷德霍姆 IDE 族一般解的新概念，并讨论了其性质。获得了双曲型偏弗雷德霍姆积分微分方程（IDE）非局部问题良好求解的必要条件和充分条件，并提供了求解算法。

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

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.