This paper presents a study of Walters’-B fluid with Caputo–Fabrizio fractional derivatives through an infinitely long oscillating vertical plate by Newtonian heating under the action of transverse magnetic field. The fractional calculus approach is employed to obtain a system of fractional partial differential equations. The governing equations of momentum and energy are converted first into dimensionless form and then solved by employing Laplace transformation. The Laplace inverse transform has been evaluated both analytically and numerically. The graphical illustrations represent the behavior of material parameters on the solutions. A comparison between exact and numerical solutions is presented in tabular and graphical form. The variation in Nusselt number with the change in fractional and physical parameters is also presented. The velocity and temperature of the fluid decreases with the enhancement in the fractional parameter for small values of time, and it has the opposite behavior for greater values of time.

本文通过牛顿加热在横向磁场的作用下，通过无限长的振荡垂直板，对具有Caputo–Fabrizio分式衍生物的Walters'B流体进行了研究。分数微积分方法用于获得分数偏微分方程组。动量和能量的控制方程首先转换为无量纲形式，然后通过使用拉普拉斯变换求解。拉普拉斯逆变换已在分析和数值上进行了评估。图形说明表示解决方案中材料参数的行为。精确解和数值解之间的比较以表格和图形形式给出。还介绍了随着分数和物理参数的变化，努塞尔数的变化。