DESIGN AND IMPLEMENTATION OF FUZZY-FRACTIONAL WU–ZHANG SYSTEM USING HE–MOHAND ALGORITHM

Fractals Pub Date : 2024-05-21 DOI:10.1142/s0218348x24400322
MUBASHIR QAYYUM, Efaza Ahmad, MUHAMMAD SOHAIL, NADIA SARHAN, EMAD MAHROUS AWWAD, A. Iqbal
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Abstract

In recent years, fuzzy and fractional calculus are utilized for simulating complex models with uncertainty and memory effects. This study is focused on fuzzy-fractional modeling of (2+1)-dimensional Wu–Zhang (WZ) system. Caputo-type time-fractional derivative and triangular fuzzy numbers are employed in the model to observe uncertainties in the presence of non-local and memory effects. The extended He–Mohand algorithm is proposed for the solution and analysis of the current model. This approach is based on homotopy perturbation method along with Mohand transformation. Effectiveness of proposed methodology at upper and lower bounds is confirmed through residual errors. The theoretical convergence of proposed algorithm is proved alongside numerical computations. Existence and uniqueness of solution are also theoretically proved in the given paper. Current investigation considers three types of fuzzifications i.e. fuzzified equations, fuzzified conditions, and finally fuzzification in both model and conditions. Different physical aspects of WZ system profiles are analyzed through 2D and 3D illustrations at upper and lower bounds. The obtained results highlight the impact of uncertainty on WZ system in fuzzy-fractional space. Hence, the proposed methodology can be used for other fuzzy-fractional systems for better accuracy with lesser computational cost.
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使用 He-mohand 算法设计和实现模糊分数吴章系统
近年来,模糊和分数微积分被用于模拟具有不确定性和记忆效应的复杂模型。本研究主要针对 (2+1)-dimensional Wu-Zhang (WZ) 系统的模糊-分数建模。模型中采用了 Caputo 型时间分式导数和三角模糊数,以观察存在非局部效应和记忆效应时的不确定性。针对当前模型的求解和分析,提出了扩展的 He-Mohand 算法。该方法基于同调扰动法和 Mohand 变换。通过残余误差确认了所提方法在上下限方面的有效性。通过数值计算证明了所提算法的理论收敛性。本文还从理论上证明了解的存在性和唯一性。目前的研究考虑了三种类型的模糊化,即模糊化方程、模糊化条件以及模型和条件的最终模糊化。通过上下限的二维和三维图解分析了 WZ 系统剖面的不同物理方面。所获得的结果凸显了模糊分数空间中不确定性对 WZ 系统的影响。因此,建议的方法可用于其他模糊分数系统,以更低的计算成本获得更高的精度。
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