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Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings 切线双曲混合纳米流体的热传输能量性能及其在聚光太阳能飞机机翼中的应用
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-03-14 DOI: 10.1515/phys-2023-0207
Adebowale Martins Obalalu, Umair Khan, Olalekan Adebayo Olayemi, Aurang Zaib, Anuar Ishak, El-Sayed M. Sherif
The primary heat source from the sunlight is solar energy (SE), which is used in photovoltaic (PV) panels, solar power plates, PV, streetlights, and solar-based hybrid nanocomposites. Currently, research is focused on analyzing and improving the efficiency of SE, particularly for powering aircraft, by combining solar power with nanotechnology advancements. As such, this study focuses on examining concentrated solar power and proposes a method to improve the performance of solar airplanes by employing nanotechnology. Furthermore, the work is based on the investigation of the flow rate, thermal distribution, and entropy generation of the magnetized tangent hyperbolic hybrid nanofluid (HNF) along the interior parabolic solar trough collector of an aircraft wing. This work utilizes similarity variables to simplify the partial derivative model into ordinary differential equations. These equations are then solved using the Galerkin weighted residual approach with the help of MATHEMATICA 11.3 software. From the obtained outcomes, it is reflected that the HNFs have high thermal conductivity than the NF. Intensification of Weissenberg number improves the performance of airplane wings subjected to heat transmission. Therefore, this research contributes to improved thermal management in advanced nanotechnology and solar aircraft.
太阳能(SE)是来自太阳光的主要热源,可用于光伏(PV)板、太阳能发电板、光伏、路灯和基于太阳能的混合纳米复合材料。目前,研究的重点是通过将太阳能与纳米技术的进步相结合,分析和提高太阳能电池的效率,特别是为飞机供电的效率。因此,本研究重点研究聚光太阳能,并提出一种通过采用纳米技术提高太阳能飞机性能的方法。此外,该研究还基于对飞机机翼内部抛物面太阳能槽集热器沿磁化切线双曲混合纳米流体(HNF)的流速、热分布和熵产生的研究。这项研究利用相似变量将偏导数模型简化为常微分方程。然后,在 MATHEMATICA 11.3 软件的帮助下,使用 Galerkin 加权残差法对这些方程进行求解。从得到的结果来看,HNF 比 NF 具有更高的热导率。韦森伯格数的增加可改善飞机机翼的传热性能。因此,这项研究有助于改进先进纳米技术和太阳能飞机的热管理。
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引用次数: 0
Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model 采用卡塔尼奥-克里斯托夫热通量和质量通量模型的第二级磁流体流过拉伸表面的对流
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-03-12 DOI: 10.1515/phys-2023-0204
Humaira Yasmin, Sana Shahab, Showkat Ahmad Lone, Zehba Raizah, Anwar Saeed
This research delves into dynamics of magnetohydrodynamic second-grade fluid flow influenced by the presence of gyrotactic microorganisms on a stretching sheet. The study takes into account various factors such as thermal radiation, chemical reactivity, and activation energy, all of which contribute to the complex behavior of fluid flow in this system. The interaction between the magnetic field and the fluid, combined with the biological aspect introduced by gyrotactic microorganisms, adds complexity to the overall analysis. The mathematical model is presented in the form of partial differential equations (PDE)s. Using the similarity variables, the modeled PDEs are transformed into ordinary differential equations. Homotopy analysis method is used for the solution of the modeled equations. After a detailed insight into this investigation, it is established that the velocity distribution declined for growth in magnetic factor and second-grade fluid parameter. The thermal characteristics are augmented for the greater values of radiation, thermophoretic and Brownian motion factors, while these profiles are weakened for upsurge in thermal relaxation time factor and Prandtl number. The concentration characteristics declined with the enhancement in Schmidt number, mass relaxation time, chemical reaction, and Brownian motion factors, while they amplified with enhancement in activation energy and thermophoresis factors. The microorganisms’ profiles are the declining functions of bioconvection Lewis and Peclet numbers. This study included a comparative analysis, which aligns closely with existing research, demonstrating a strong concordance with established findings.
本研究深入探讨了受拉伸片上陀螺状微生物存在影响的磁流体二级流体流动动力学。研究考虑了各种因素,如热辐射、化学反应性和活化能,所有这些因素都导致了该系统中流体流动的复杂行为。磁场与流体之间的相互作用,再加上陀螺触动微生物引入的生物因素,增加了整体分析的复杂性。数学模型以偏微分方程(PDE)的形式呈现。利用相似变量,将建模的偏微分方程转换为常微分方程。模型方程的求解采用了同调分析方法。在对这一研究进行详细了解后,确定速度分布随着磁性因子和二级流体参数的增长而下降。辐射因子、热泳因子和布朗运动因子的数值越大,热特性就越强,而热弛豫时间因子和普朗特数的数值越大,这些特性就越弱。浓度特征随着施密特数、质量弛豫时间、化学反应和布朗运动因子的增加而减弱,但随着活化能和热泳因子的增加而增强。微生物曲线是生物对流路易斯数和佩克雷数的递减函数。这项研究包括一项比较分析,它与现有研究密切吻合,显示出与已有研究结果的高度一致性。
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引用次数: 0
Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations 二维非恒定系数平流扩散方程离散化某些方案的稳定性分析和数值结果
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-03-12 DOI: 10.1515/phys-2023-0195
Appanah Rao Appadu, Hagos Hailu Gidey
We solve two numerical experiments described by 2D nonconstant coefficient advection–diffusion equations with specified initial and boundary conditions. Three finite difference methods, namely Lax–Wendroff, Du-Fort–Frankel and a nonstandard finite difference scheme, are derived and used to solve the two problems, whereby only the first problem has an exact solution. Stability analysis is performed to obtain a range of values of the time step size at a fixed spatial step size. We obtain the rate of convergence in space when the three methods are used to solve Problem 1. Computational times of the three algorithms are computed for Problem 1. Results are displayed for the two problems using the three methods at times T = 1.0 T=1.0 and T = 5.0 T=5.0 . The main novelty is the stability analysis, which is not straightforward as we are working with numerical methods discretising 2D nonconstant coefficient advection–diffusion equation where many parameters are involved. The second highlight is to determine the most efficient scheme from the three methods. Third, there are very few published studies on analysis and use of numerical methods to solve nonconstant coefficient advection–diffusion equations, and this is one of the very few rare articles treating such topics.
我们求解了两个由二维非恒定系数平流扩散方程描述的数值实验,并指定了初始条件和边界条件。推导出三种有限差分方法,即 Lax-Wendroff、Du-Fort-Frankel 和非标准有限差分方案,并用于求解这两个问题,其中只有第一个问题有精确解。我们进行了稳定性分析,以获得在固定空间步长下时间步长的取值范围。当使用这三种方法求解问题 1 时,我们得到了空间收敛速率。针对问题 1 计算了三种算法的计算时间。结果显示了在时间 T=1.0 T=1.0 和 T=5.0 T=5.0 时使用三种方法解决两个问题的结果。主要的新颖之处在于稳定性分析,这并不简单,因为我们使用的是离散二维非定常系数平流扩散方程的数值方法,其中涉及许多参数。第二个亮点是从三种方法中确定最有效的方案。第三,关于分析和使用数值方法求解非定常系数平流-扩散方程的公开研究很少,这篇文章是极少数处理此类主题的文章之一。
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引用次数: 0
Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents 带热源/散热器和反应剂的拉伸圆柱体上银/金纳米颗粒混合纳米流体漩涡流动的优化框架数值解决方案
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-03-12 DOI: 10.1515/phys-2023-0202
Humaira Yasmin, Showkat Ahmad Lone, Ali M. Mahnashi, Waleed Hamali, M. D. Shamshuddin, Anwar Saeed
The heat and mass transportation for nanofluid across a swirling cylinder under the actions of magnetic effects and Cattaneo–Christov heat flux is reported in the current analysis. The objective of this study is to examine the energy and mass transmissions through hybrid nanofluid under the influence of heat source/sink and reactive species. The hybrid nanoliquid has been prepared by the dispersion of silver (Ag) and gold (Au) nanoparticles (NPs) in the base fluid ethylene glycol (C2H6O2). The flow phenomena are expressed in the form of nonlinear partial differential equations and are converted to a nondimensional form, by employing the similarity substitution. For the computational estimation of the problem, the parametric continuation method is employed. The demonstration of velocity, mass, and energy outlines versus distinct physical factors is exposed in the form of figures. It has been perceived that the axial and swirling velocity outline drops with the influence of the Reynolds number, magnetic effect, and the insertion of Au and Ag NPs in C2H6O2. Furthermore, the hybrid nanofluid energy curve declines with the effect of the Reynolds number, thermal relaxation factor, and the volume friction of NPs.
目前的分析报告了纳米流体在磁效应和卡塔尼奥-克里斯托夫热通量作用下穿过漩涡圆柱体的热量和质量传输。本研究的目的是考察混合纳米流体在热源/热沉和反应物影响下的能量和质量传输。混合纳米流体是由银(Ag)和金(Au)纳米粒子(NPs)分散在基础流体乙二醇(C2H6O2)中制备而成。流动现象以非线性偏微分方程的形式表示,并通过相似性替换转换为非维度形式。为了对问题进行计算估算,采用了参数延续法。速度、质量和能量轮廓与不同物理因素的关系以图表的形式展示出来。研究发现,随着雷诺数、磁效应以及在 C2H6O2 中加入 Au 和 Ag NPs 的影响,轴向和漩涡速度轮廓下降。此外,混合纳米流体的能量曲线随着雷诺数、热弛豫因子和 NPs 体积摩擦的影响而下降。
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引用次数: 0
Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications 提高 Al2O3、ZnO 和 TiO2 二元纳米流体在传热应用中的稳定性
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-03-05 DOI: 10.1515/phys-2023-0199
Ans Ahmed Memon, Laveet Kumar, Abdul Ghafoor Memon, Khanji Harijan, Zafar Said
Primary goal of this research is to enhance stability of nanofluids which is vital for maintaining consistent thermophysical properties during various applications. Nanofluid stability is essential for obtaining the uniform thermophysical properties during its application. X-ray diffraction and zeta potential were performed to characterize three nanoparticles, namely TiO2, Al2O3, and ZnO. Experimental work was carried out under several trials to enhance the stability of nanofluids. Initially, deionized water was used as base fluid for stability analysis, but nanoparticles agglomerate within after 5 h. Second, alkaline water was selected as base fluid at different pHs ranging from 7 to 14 to analyze the stability of the nanofluids. Finally, the effect of surfactant addition on the stability of prepared nanofluids was also investigated. Observations revealed that at pH 11, nanoparticles exhibited enhanced stability compared to other pH levels. This stability can be attributed to the high zeta potential, fostering electrostatic repulsion between individual particles. It was concluded from the results that zeta potential increases in cases of (TiO2 + ZnO) and (Al2O3 + ZnO) from −44.2 to −47.8 mV and −42.4 to −44.1 mV with the addition of surfactant, respectively. In the case of (Al2O3 + TiO2), zeta potential decreases slightly from −47.7 to −44.9 mV with the addition of surfactant.
这项研究的主要目标是提高纳米流体的稳定性,这对于在各种应用中保持一致的热物理性质至关重要。纳米流体的稳定性对于在应用过程中获得均匀的热物理性质至关重要。X 射线衍射和 zeta 电位对三种纳米粒子(即 TiO2、Al2O3 和 ZnO)进行了表征。为了提高纳米流体的稳定性,实验工作经过了多次试验。最初,实验使用去离子水作为基液进行稳定性分析,但纳米粒子在 5 小时后就会聚集。其次,实验选择碱性水作为基液,在 7 至 14 的不同 pH 值范围内分析纳米流体的稳定性。最后,还研究了添加表面活性剂对制备的纳米流体稳定性的影响。观察结果表明,与其他 pH 值相比,纳米粒子在 pH 值为 11 时表现出更高的稳定性。这种稳定性可归因于高 zeta 电位促进了单个颗粒之间的静电排斥。结果表明,添加表面活性剂后,(TiO2 + ZnO)和(Al2O3 + ZnO)的 zeta 电位分别从 -44.2 mV 上升到 -47.8 mV 和 -42.4 mV 上升到 -44.1 mV。加入表面活性剂后,(Al2O3 + TiO2)的 zeta 电位略有下降,从 -47.7 mV 降至 -44.9 mV。
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引用次数: 0
Chaotic control problem of BEC system based on Hartree–Fock mean field theory 基于哈特里-福克均值场理论的 BEC 系统混沌控制问题
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-03-01 DOI: 10.1515/phys-2023-0196
Yang Shen, Meng Xu
Due to the difficulty of studying nonlinear quantum systems and the unique composition of Bose–Einstein condensate (BEC) systems, BECs face significant difficulties in solving dynamic analysis and chaotic control problems. Therefore, Hartree–Fock mean field theory is introduced to study the chaotic characteristics, control, and synchronization issues of BEC systems loaded on optical lattices. First, the stability and chaos of BECs in optical lattices were analyzed. Subsequently, constant shift method and activation control were introduced based on the Gross–Pitaevskii equation to achieve control and synchronization of the BEC system. Second, based on the Lyapunov exponent theory, offset parameters are added to BEC chaotic control to achieve control of particle density. Finally, based on the stability theory of linear systems, a control term is introduced to achieve variable analysis of the system’s drive–response system, ensuring that chaotic systems with different initial conditions can still achieve good synchronization and anti-synchronization control. The chaotic problem of BEC system was analyzed using numerical and theoretical methods in the experiment. The effect of adjusting the parameters of the BEC system under the constant shift method is significant. The system exhibits a chaotic state under the Lyapunov exponent, which is mainly concentrated between [3.4, 4.5], demonstrating good system stability. When the offset constant range is [4.21, 5.67], the maximum Lyapunov exponent value is below 0. In the problem of chaotic synchronization, adding activation control causes the system’s time series to exhibit anti-synchronization with spatiotemporal variable variation, while adding control terms leads the system to tend towards synchronization and anti-synchronization with time evolution. The analysis of chaotic control problems in BEC systems can provide reference value and theoretical basis for the dynamic research of quantum physics and related nonlinear systems.
由于研究非线性量子系统的难度和玻色-爱因斯坦凝聚态(BEC)系统的独特组成,BEC 在解决动态分析和混沌控制问题时面临很大困难。因此,本文引入哈特里-福克均场理论来研究加载在光学晶格上的 BEC 系统的混沌特性、控制和同步问题。首先,分析了光晶格中 BEC 的稳定性和混沌性。随后,基于 Gross-Pitaevskii 方程引入了恒定位移法和激活控制,以实现对 BEC 系统的控制和同步。其次,基于李雅普诺夫指数理论,在 BEC 混沌控制中加入偏移参数,实现对粒子密度的控制。最后,基于线性系统稳定性理论,引入控制项,实现系统驱动-响应系统的变量分析,确保不同初始条件下的混沌系统仍能实现良好的同步和反同步控制。实验中采用数值和理论方法分析了 BEC 系统的混沌问题。在恒定位移法下,调整 BEC 系统参数的效果显著。系统在 Lyapunov 指数下呈现混沌状态,主要集中在 [3.4, 4.5] 之间,表现出良好的系统稳定性。当偏移常数范围为[4.21,5.67]时,最大 Lyapunov 指数值低于 0。在混沌同步问题中,加入激活控制会使系统的时间序列随时空变量变化呈现反同步,而加入控制项则会使系统随时间演化趋于同步和反同步。对 BEC 系统混沌控制问题的分析,可为量子物理及相关非线性系统的动力学研究提供参考价值和理论依据。
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引用次数: 0
Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests 基于多批试验的正态寿命分布设备可靠性贝叶斯估算
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-02-28 DOI: 10.1515/phys-2023-0188
Haobang Liu, Tao Hu, Tong Chen, Minggui Li, Kai Du
The test of new equipment is usually carried out in multiple batches according to the task schedule and test results. Constrained by the test environment, cost, and other factors, the amount of reliability test data in each batch is relatively limited, which brings difficulties to the accurate equipment reliability estimation work. For the reliability simulation tests conducted before each batch tests, it is particularly important to make full use of each batch tests information and simulation tests information to estimate the reliability of the equipment for small sample tests. This study takes the common normal-type life distribution equipment as the research object, and selects the normal-inverse gamma distribution as the equipment life parameters prior distribution based on the Bayesian method. Combined with the system contribution, the fusion weights of each batch tests information are determined and all the batch tests information is fused. Finally, the estimation of equipment reliability based on multiple batch tests is completed. The research results show that this method can integrate the information of each batch test and simulation test, overcome the problem of insufficient information of single batch tests, and provide an effective analytical tool for equipment reliability estimation.
新设备的试验通常根据任务计划和试验结果分多批进行。受试验环境、成本等因素的制约,每批次的可靠性试验数据量相对有限,这给设备可靠性的精确估算工作带来了困难。对于每批次试验前进行的可靠性模拟试验,充分利用每批次试验信息和模拟试验信息对设备进行小样本试验可靠性估算显得尤为重要。本研究以常见的正态型寿命分布设备为研究对象,基于贝叶斯方法选取正态-反γ分布作为设备寿命参数的先验分布。结合系统贡献,确定各批次试验信息的融合权重,并对所有批次试验信息进行融合。最后,完成基于多批次试验的设备可靠性估算。研究结果表明,该方法能够融合各批次试验和模拟试验的信息,克服了单批次试验信息不足的问题,为设备可靠性估算提供了有效的分析工具。
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引用次数: 0
Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas 天然气螺旋缠绕式热交换器的流动和传热性能数值研究
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-02-28 DOI: 10.1515/phys-2023-0189
Wang Ya-bin, Ma Yang-fan, Zhang Qian, Zhou Yan, Ma Ting, Shi Yu, Zeng Min
The spiral-wound heat exchanger is a key equipment in the liquefied natural gas application, but the flow and heat transfer mechanisms remain unclarified. In this study, a three-dimensional numerical model is created, focusing on exploring the impact of four crucial structural parameters on the flow and heat transfer performance of natural gas, including the external diameter of tubes, the diameter of the core cylinder, the longitudinal pitch of tubes in the same layer, and the radial pitch of tube bundles between the adjacent layer. It was found that the tube diameter, core cylinder diameter, and radial pitch had significant effects on Nu and Δp m. The optimal Nu on the shell side was obtained at medium core cylinder size. The longitudinal pitch had a weak effect on the performance of both sides, and the longitudinal pitch corresponding to the maximum values of Nu and Δp m on both sides increased with the increase in the inlet Reynolds number. Under the effect of centrifugal force, a shifted tendency was shown by the velocity and temperature fields.
螺旋缠绕式换热器是液化天然气应用中的关键设备,但其流动和传热机理仍未阐明。本研究建立了一个三维数值模型,重点探讨了四个关键结构参数对天然气流动和传热性能的影响,包括管子外径、芯筒直径、同层管子纵向间距和相邻层间管束径向间距。结果发现,管子直径、芯筒直径和径向间距对 Nu 和 Δp m 有显著影响。纵向螺距对两侧性能的影响较弱,两侧 Nu 和 Δp m 最大值所对应的纵向螺距随入口雷诺数的增加而增大。在离心力的作用下,速度场和温度场出现了移动趋势。
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引用次数: 0
Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks 无线传感器网络中多软件攻击的动态特性无线传感器网络的分数导数分析
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-02-26 DOI: 10.1515/phys-2023-0190
Hassan Tahir, Anwarud Din, Kamal Shah, Maggie Aphane, Thabet Abdeljawad
Due to inherent operating constraints, wireless sensor networks (WSNs) need help assuring network security. This problem is caused by worms entering the networks, which can spread uncontrollably to nearby nodes from a single node infected with computer viruses, worms, trojans, and other malicious software, which can compromise the network’s integrity and functionality. This article discusses a fractional S E 1 E 2 I R {mathsf{S}}{{mathsf{E}}}_{1}{{mathsf{E}}}_{2}{mathsf{I}}{mathsf{R}} model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. To illustrate our analytical conclusions, we ran numerical simulations.
由于固有的运行限制,无线传感器网络(WSN)需要帮助确保网络安全。造成这一问题的原因是蠕虫进入网络,感染计算机病毒、蠕虫、木马和其他恶意软件的单个节点会不受控制地向附近的节点传播,从而破坏网络的完整性和功能。本文讨论了一个分数 S E 1 E 2 I R {mathsf{S}}{{mathsf{E}}_{1}{{mathsf{E}}_{2}{mathsf{I}}{mathsf{R}} 模型来解释 WSN 中的蠕虫传播。为了捕捉病毒的动态变化,我们使用了 Mittag-Leffler 核和 Atangana-Baleanu (AB) Caputo 算子。除了问题的其他特征外,我们还研究了 AB 卡普托导数的叠加和 Lipschitzness 特性。采用标准数值方法对阿坦加纳-巴莱阿努-卡普托分数导数进行了近似,并给出了详细分析。为了说明我们的分析结论,我们进行了数值模拟。
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引用次数: 0
Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator 用 Atangana-Baleanu 算子分析模糊分数 Degasperis-Procesi 和 Camassa-Holm 方程
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-02-23 DOI: 10.1515/phys-2023-0191
Azzh Saad Alshehry, Humaira Yasmin, Manzoor Ali Shah, Rasool Shah
This article presents a new approach for solving the fuzzy fractional Degasperis–Procesi (FFDP) and Camassa–Holm equations using the iterative transform method (ITM). The fractional Degasperis–Procesi (DP) and Camassa–Holm equations are extended from the classical DP and Camassa–Holm equations by incorporating fuzzy sets and fractional derivatives. The ITM is a powerful technique widely used for solving nonlinear differential equations. This approach transforms the fuzzy fractional differential equations into a series of ordinary differential equations, which are then solved iteratively using a recursive algorithm. Numerical simulations demonstrate the proposed approach’s accuracy and effectiveness. The results show that the ITM provides an efficient and accurate method for solving the FFDP and Camassa–Holm equations. The proposed method can be extended to solve other fuzzy fractional differential equations.
本文提出了一种利用迭代变换法(ITM)求解模糊分数德加斯佩里斯-普罗切斯方程(FFDP)和卡马萨-霍姆方程的新方法。分数 Degasperis-Procesi (DP) 和 Camassa-Holm 方程是在经典 DP 和 Camassa-Holm 方程的基础上结合模糊集和分数导数扩展而来的。ITM 是一种广泛用于求解非线性微分方程的强大技术。这种方法将模糊分数微分方程转化为一系列常微分方程,然后使用递归算法迭代求解。数值模拟证明了所提出方法的准确性和有效性。结果表明,ITM 为求解 FFDP 和 Camassa-Holm 方程提供了一种高效、精确的方法。所提出的方法还可扩展用于求解其他模糊分微分方程。
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引用次数: 0
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Open Physics
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