涉及收敛级数和时变奇点的微分问题解的唯一性、稳定性和模拟

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-08-01 DOI:10.1216/rmj.2023.53.1099

Yazid Gouari, Zoubir Dahmani, Meriem Mansouria Belhamiti, Mehmet Zeki Sarikaya

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引用次数: 0

摘要

研究了一类具有非局部积分条件的非线性积分微分方程的新问题。所考虑的问题在时间轴原点是奇异的，它涉及到收敛级数与黎曼-刘维尔积分的结合。我们证明了问题的一个存在唯一性结果。给出了一些例子来说明唯一性结果。研究了该问题的Ulam-Hyers稳定性。然后，由于一些数值技术，使我们能够近似卡普托导数，并通过使用龙格-库塔方法，我们提出了一个数值研究与一些模拟，以显示更多的理解所提出的例子。

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查看原文本刊更多论文

UNIQUENESS OF SOLUTIONS, STABILITY AND SIMULATIONS FOR A DIFFERENTIAL PROBLEM INVOLVING CONVERGENT SERIES AND TIME VARIABLE SINGULARITIES

We study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series combined with Riemann–Liouville integrals. We prove an existence and uniqueness result for our problem. Some examples are given to illustrate the uniqueness result. The Ulam–Hyers stability for the problem is also studied. Then, thanks to some numerical techniques, that allow us to approximate the Caputo derivatives, and by using the Runge–Kutta method, we present a numerical study with some simulations to show more comprehension of the proposed examples.

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.