This paper is devoted to introduce an efficient solver using the Hermite collocation technique (HCT), of the coupled system of fractional differential equations (FDEs). The given systems are of basic importance in modeling various phenomena like Cascades and Compartment Analysis, Pond Pollution, Home Heating, Chemostats, and Microorganism Culturing, Nutrient Flow in an Aquarium, Biomass Transfer, Forecasting Prices, Electrical Network, Earthquake Effects on Buildings. The proposed method reduces the system of FDEs to a system of algebraic equations in the coefficients of the expansion using the Hermite polynomials. The introduced method is computer oriented and provides highly accurate solution. To demonstrate the efficiency of the method, two examples are solved and the results are displayed graphically. Finally, we convert the presented coupled systems from the case of its standard form to a first-order ordinary differential equations to compare the obtained numerical solutions with those solutions using the fourth-order Runge–Kutta method (RK4).

中文翻译：

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获取非线性FDEs耦合系统混沌行为的Hermite搭配方法

本文致力于介绍使用 Hermite 搭配技术 (HCT) 的分数微分方程 (FDE) 耦合系统的高效求解器。给定的系统对于模拟各种现象至关重要，例如级联和隔间分析、池塘污染、家庭供暖、恒化器和微生物培养、水族馆中的营养流动、生物质转移、预测价格、电网、地震对建筑物的影响。所提出的方法使用 Hermite 多项式将 FDE 系统简化为膨胀系数中的代数方程组。所介绍的方法是面向计算机的，并提供了高度准确的解决方案。为了证明该方法的效率，解决了两个示例，并以图形方式显示了结果。最后，