This paper proposes an advanced numerical-analytical approach for handling a class of fuzzy fractional differential equations involving Caputo-Fabrizio derivative with a non-singular kernel arsing in the medical sector. The solution methodology relies on the reproducing-kernel algorithm to generate analytical solutions in the form of a uniformly convergent series in the direct sum of the desired Hilbert spaces. The effectiveness of the method is analyzed by studying some theoretical, analytical, and stability results of the derived solutions based on the reproducing kernel theory. Numerical simulations are also provided in tables and graphs to demonstrate the reliability of this algorithm in solving fuzzy models using the new Caputo-Fabrizio fractional operator, especially for the drug pharmacokinetic model. The obtained results show the ability of the applied algorithm to solve a wide range of nonlinear fractional models emerging in pharmacology, medicine, and biochemistry.

本文提出了一种先进的数值分析方法，用于处理一类涉及Caputo-Fabrizio导数的模糊分数阶微分方程，在医疗领域该算法具有非奇异核。解方法论依靠复制核算法在所需希尔伯特空间的直接总和中以一致收敛序列的形式生成解析解。通过研究基于重现核理论的导出解决方案的一些理论，分析和稳定性结果，分析了该方法的有效性。在表格和图表中还提供了数值模拟，以证明该算法在使用新型Caputo-Fabrizio分数算符求解模糊模型时的可靠性，尤其是对于药物药代动力学模型而言。