We propose a novel dynamical model for blood alcohol concentration that incorporates $\psi$-Caputo fractional derivatives. Using the generalized Laplace transform technique, we successfully derive an analytic solution for both the alcohol concentration in the stomach and the alcohol concentration in the blood of an individual. These analytical formulas provide us a straightforward numerical scheme, which demonstrates the efficacy of the $\psi$-Caputo derivative operator in achieving a better fit to real experimental data on blood alcohol levels available in the literature. In comparison to existing classical and fractional models found in the literature, our model outperforms them significantly. Indeed, by employing a simple yet non-standard kernel function $\psi(t)$, we are able to reduce the error by more than half, resulting in an impressive gain improvement of 59 percent.

翻译：我们提出了一种基于$\psi$-Caputo分数阶导数的血液酒精浓度新型动力学模型。利用广义拉普拉斯变换技术，我们成功推导出个体胃中酒精浓度和血液中酒精浓度的解析解。这些解析公式提供了一种直接的数值方案，证明了$\psi$-Caputo导数算子能更好地拟合文献中已有的真实血液酒精水平实验数据。与文献中现有的经典模型和分数阶模型相比，我们的模型显著优于它们。实际上，通过采用简单但非标准的核函数$\psi(t)$，我们能够将误差减少一半以上，实现了59%的显著改进增益。