不同应用的时间分数阶Klein-Gordon方程新解

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引用次数: 0

摘要

本文首次将拉普拉斯变换与同伦摄动方法相结合的拉普拉斯同伦摄动方法(LHPM)用于求解非线性时间分数阶Klein-Gordon (TFKG)方程。也就是说,在文献中首次将LHPM用于求解非线性TFKG方程。首先,开发了具有Caputo分数阶导数的TFKG上的LHPM程序。此外,本文还对两个不同的实例进行了LHPM方法的应用。这反过来证明了所提出的方法的通用性。此外,通过将两个算例的数值解与精确解进行比较,证明了该方法的有效性。最后,通过对各算例计算的相对误差进行比较,验证了所提方法在TFKG方程上的效率和有效性。
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Novel Solution for Time-fractional Klein-Gordon Equation with Different Applications
In this paper, for the first time, the Laplace Homotopy Perturbation Method (LHPM), which is the coupling of the Laplace transform and the Homotopy Perturbation Method, is employed to solve non-linear time-fractional Klein-Gordon (TFKG) equations. In other words, for the first time in literature, LHPM is used to solve non-linear TFKG equations. First of all, the procedure of LHPM on TFKG with Caputo fractional derivative is developed. Further, the developed approach of LHPM on TFKG is used for two different examples. This in turn proves the versatile nature of the proposed method. In addition, the validity of the approach is proved by comparing the numerical solutions of both examples with their exact solution. Finally, the comparison of relative errors calculated in each example proves the efficiency and effectiveness of the proposed method on TFKG equations.
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来源期刊
CiteScore
3.80
自引率
6.20%
发文量
57
审稿时长
20 weeks
期刊介绍: IJMEMS is a peer reviewed international journal aiming on both the theoretical and practical aspects of mathematical, engineering and management sciences. The original, not-previously published, research manuscripts on topics such as the following (but not limited to) will be considered for publication: *Mathematical Sciences- applied mathematics and allied fields, operations research, mathematical statistics. *Engineering Sciences- computer science engineering, mechanical engineering, information technology engineering, civil engineering, aeronautical engineering, industrial engineering, systems engineering, reliability engineering, production engineering. *Management Sciences- engineering management, risk management, business models, supply chain management.
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