This paper deals with a set of three partial differential equations involving time-fractional derivatives and nonlinear diffusion operators. This model helps us to understand the HIV spread and transmission into the patient. First, we prove the existence and uniqueness of weak solutions to the mathematical model. Then, the Galerkin finite element scheme is implemented to approximate the solution of the model. Further, a-priori error bounds and convergence estimates for the fully-discrete problem are derived. The second order convergence for the proposed scheme is also proved. Numerical tests are shown to validate the theoretical studies.

中文翻译：

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具有非线性扩散的时间分数HIV感染模型

本文涉及一组三个包含时间分数导数和非线性扩散算子的偏微分方程。该模型有助于我们了解艾滋病毒在患者中的传播和传播情况。首先，我们证明了该数学模型的弱解的存在性和唯一性。然后，采用Galerkin有限元方案来近似模型的解。此外，推导了完全离散问题的先验误差范围和收敛估计。还证明了所提方案的二阶收敛性。数值试验证明了理论研究的正确性。