This paper is devoted to develop a new mathematical model for Alzheimer disease based on a system of fractional-order partial differential equations. The system of Alzheimer disease includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid $\beta$ aggregation and hyperphosphorylated tau proteins. We consider the Caputo fractional derivative definition to analyze the formulated system by simulating the effect of drugs that either failed or currently in clinical trials. To simulate the model, we use tight frame (framelet) systems generated using the unitaryand oblique extension principle. According to the simulation results, and based on using such new direction of fractional modeling, the progression of Alzheimer disease and its consequences will be slowing down. Which may give clinical insights on intervention measures against the disease and its effective therapies.

本文致力于建立基于分数阶偏微分方程组的阿尔茨海默病新数学模型。阿尔茨海默氏病系统包括神经元，星形胶质细胞，小胶质细胞和外周巨噬细胞，以及淀粉样蛋白$\beta$聚集和过度磷酸化的tau蛋白。我们考虑Caputo分数导数定义，通过模拟药物失败或目前在临床试验中的药物作用来分析配方系统。为了模拟模型，我们使用了采用the斜扩展原理生成的紧框架（小框架）系统。根据模拟结果，并基于分数建模的这种新方向，阿尔茨海默病的进展及其后果将放慢。这可能会为针对该疾病及其有效疗法的干预措施提供临床见解。