With the help of Banach’s fixed-point approach and the Leray–Schauder alternative theorem, we produced existence results for a general class of fractional differential equations in this paper. The proposed problem is more comprehensive and applicable to real-life situations. As an example of how our problem might be used, we have created a fractional-order COVID-19 model whose solution is guaranteed by our results. We employed a numerical approach to solve the COVID-19 model, and the results were compared for different fractional orders. Our numerical results for fractional orders follow the same pattern as the classical example of order 1, indicating that our numerical scheme is accurate.

中文翻译：

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应用于生物系统的分数阶序列混合系统

借助 Banach 的不动点方法和 Leray-Schauder 替代定理，我们得到了本文中一类一般分数阶微分方程的存在性结果。所提出的问题更全面，更适用于现实生活中的情况。作为如何使用我们的问题的示例，我们创建了一个分数阶 COVID-19 模型，其解决方案由我们的结果保证。我们采用数值方法来求解 COVID-19 模型，并比较了不同分数阶的结果。我们的分数阶数值结果遵循与 1 阶经典示例相同的模式，表明我们的数值方案是准确的。