用卡普托导数的自然变换半解析逼近时间分数电报方程

IF 2.4 Q2 ENGINEERING, MECHANICAL

Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0289

Mamta Kapoor, Samanyu Khosla

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引用次数: 2

摘要

摘要本文采用自然变换在一维、二维和三维上迭代求解时间分数型双曲电报方程。分数阶导数是在卡普托意义上考虑的。这些方程为电脉冲信号处理和传输的波动理论过程提供了一个模型。为了评估建议策略的有效性和有效性，对近似结果和精确结果进行了图形比较。利用L∞{L＿}{\infty对逼近}进行了收敛性分析。所提出的方法可以成功且无误差地求解各种常微分方程、偏微分方程、分数阶偏微分方程和分数阶双曲电报方程。图形摘要

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Semi-analytical approximation of time-fractional telegraph equation via natural transform in Caputo derivative

Abstract In the present research study, time-fractional hyperbolic telegraph equations are solved iteratively using natural transform in one, two, and three dimensions. The fractional derivative is considered in the Caputo sense. These equations serve as a model for the wave theory process of signal processing and transmission of electric impulses. To evaluate the validity and effectiveness of the suggested strategy, a graphical comparison of approximated and exact findings is performed. Convergence analysis of the approximations utilising L ∞ {L}_{\infty } has been done using tables. The suggested approach may successfully and without errors solve a wide variety of ordinary differential equations, partial differential equations (PDEs), fractional PDEs, and fractional hyperbolic telegraph equations. Graphical abstract

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来源期刊

Nonlinear Engineering - Modeling and Application Multiple-

CiteScore

6.20

自引率

3.60%

发文量

审稿时长

44 weeks

期刊介绍： The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.