Extracting the Ultimate New Soliton Solutions of Some Nonlinear Time Fractional PDEs via the Conformable Fractional Derivative

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Md Ashik Iqbal, A. Ganie, M. M. Miah, M. S. Osman
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引用次数: 0

Abstract

Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are the time-fractional Klein–Gordon equation (KGE), the time-fractional Sharma–Tasso–Olever equation (STOE), and the time-fractional Clannish Random Walker’s Parabolic equation (CRWPE). These models were investigated by using an expansion method for extracting new soliton solutions. Two types of results were found: one was trigonometric and the other one was an exponential form. For a profound explanation of the physical phenomena of the studied fractional models, some results were graphed in 2D, 3D, and contour plots by imposing the distinctive results for some parameters under the oblige conditions. From the numerical investigation, it was noticed that the obtained results referred smooth kink-shaped soliton, ant-kink-shaped soliton, bright kink-shaped soliton, singular periodic solution, and multiple singular periodic solutions. The results also showed that the amplitude of the wave augmented with the pulsation in time, which derived the order of time fractional coefficient, remarkably enhanced the wave propagation, and influenced the nonlinearity impacts.
通过可变分式衍生物提取某些非线性时间分式多线性方程的终极新孤子解
非线性分数阶微分方程在应用科学和分数工程的各个分支中发挥着重要作用。本研究论文展示了三个此类分数数学模型的实际应用,它们是时间分数克莱因-戈登方程(KGE)、时间分数夏尔马-塔索-奥勒弗方程(STOE)和时间分数克兰尼什随机沃克抛物线方程(CRWPE)。研究人员使用扩展方法对这些模型进行了研究,以提取新的孤子解。研究发现了两种结果:一种是三角函数形式,另一种是指数形式。为了深入解释所研究的分数模型的物理现象,通过在强制条件下对某些参数施加不同的结果,在二维、三维和等值线图中绘制了一些结果。从数值研究中可以发现,所得到的结果涉及光滑 "疙瘩 "形孤子、蚂蚁 "疙瘩 "形孤子、明亮 "疙瘩 "形孤子、奇异周期解和多奇异周期解。结果还表明,波的振幅随时间脉动而增大,从而衍生出时间分数系数阶次,显著增强了波的传播,并影响了非线性影响。
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
CiteScore
7.20
自引率
4.30%
发文量
567
期刊介绍: ACS Applied Electronic Materials is an interdisciplinary journal publishing original research covering all aspects of electronic materials. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials science, engineering, optics, physics, and chemistry into important applications of electronic materials. Sample research topics that span the journal's scope are inorganic, organic, ionic and polymeric materials with properties that include conducting, semiconducting, superconducting, insulating, dielectric, magnetic, optoelectronic, piezoelectric, ferroelectric and thermoelectric. Indexed/​Abstracted: Web of Science SCIE Scopus CAS INSPEC Portico
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