In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

在本文中，我们在微通道中使用 Caputo 分数阶导数构建了 Burgers 流体的瞬态电渗流，其中泊松-玻尔兹曼方程描述了沿微通道长度施加的势电场。得到速度剖面分量的解析解，首先应用拉普拉斯变换结合偏微分方程的经典方法，然后应用拉普拉斯变换结合有限傅立叶正弦变换。温度分量的精确解是通过应用拉普拉斯变换和有限傅立叶正弦变换获得的。此外，由于速度和温度控制方程的导出模型的复杂性，借助基于Stehfest算法的数值反演公式，借助MATHCAD软件，得到了拉普拉斯逆变换。展示并分析了时间、延迟时间、电动宽度和分数参数对流体流动速度的影响以及时间和分数参数对微通道中温度分布的影响的图形表示。结果表明，外加电场、电渗力、电动宽度和弛豫时间对微通道中的速度分布起着至关重要的作用。分数参数可用于调节微通道中的速度和温度。该研究可用于设计各种生物医学芯片实验室设备，