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.

近年来，模糊和分数阶微积分被用来模拟具有不确定性和记忆效应的复杂模型。本研究的重点是 (2+1) 维 Wu-Zhang (WZ) 系统的模糊分数建模。模型中采用卡普托型时间分数阶导数和三角模糊数来观察非局部效应和记忆效应存在的不确定性。提出了扩展的He-Mohand算法来求解和分析当前模型。该方法基于同伦微扰法和莫汉德变换。所提出的方法在上限和下限的有效性通过残余误差得到证实。通过数值计算证明了所提出算法的理论收敛性。论文还从理论上证明了解的存在性和唯一性。当前的研究考虑了三种类型的模糊化，即模糊化方程、模糊化条件以及最终的模型和条件模糊化。通过上限和下限的 2D 和 3D 插图分析了 WZ 系统轮廓的不同物理方面。获得的结果突出了模糊分数空间中不确定性对 WZ 系统的影响。因此，所提出的方法可用于其他模糊分数系统，以更少的计算成本获得更高的精度。