The main aim of this study is to apply the recent definition of fractional derivative i.e. Atangana-Baleanu time-fractional derivative on second grade fluid flowing on an infinite plate under the MHD (magnetohydrodynamics) effect. The flow is studied under both Darcy's law and heat transfer. To find out the analytical solution, the Laplace transformation technique is utilized on the obtained non-dimensional governing equations momentum and heat equations with initial and boundary conditions. To enhance the innovation of this study, the graphical and numerical comparison of heat and momentum equation is analyzed with different parameters for different values. Main results and conclusions are accomplished at the end of this work. The increasing change in temperature profile is noticed with fractional parameter and Grashof number. The velocity profile increases with the Prandtl number while a reverse trend is noted for the temperature profile.

本研究的主要目的是应用分数导数的最新定义，即 Atangana-Baleanu 时间分数导数，用于在 MHD（磁流体动力学）效应下在无限板上流动的二级流体。在达西定律和传热下研究流动。为了找出解析解，对获得的具有初始和边界条件的无量纲控制方程动量和热方程使用拉普拉斯变换技术。为增强本研究的创新性，对不同参数、不同取值的热动量方程进行图形和数值比较分析。主要结果和结论在这项工作结束时完成。通过分数参数和 Grashof 数注意到温度分布的增加变化。