Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0230

N. Alharthi, A. Atangana, B. Alkahtani

引用次数: 0

Abstract

Abstract Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.

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非局部算符阻尼谐振子模型的解析与数值分析

摘要本文采用不同核的非局部算子来得到更一般的谐振子模型。利用幂律、指数衰减和具有Delta-Dirac性质的广义mitag - leffler核。本研究的目的是在阻尼谐振子模型中引入与上述核相关的非定域，并在计算由拉普拉斯变换和Sumudu变换得到的波德图时，观察每一个核的影响。对于每种情况，我们同时应用拉普拉斯变换和Sumudu变换来获得复空间中的解。对于每种情况，我们得到了不同分数阶值的波德图和相图。我们给出了唯一性的详细分析和精确解，并使用数值逼近得到数值解。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.