The prime concern of this study is to analyze the generalized time-dependent magnetohydrodynamic (MHD) slip transport of an Oldroyd-B fluid near an oscillating upright plate. The plate is nested in a porous media under the action of ramped heating and nonlinear thermal radiation. Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) derivatives are utilized to constitute fractional partial differential equations that establish slip flow, shear stress, and heat transfer phenomena. Primarily, Laplace transformation is applied to dimensionless fractional models, and later Stehfest’s numerical algorithm is invoked to anticipate solutions of momentum and heat equations in principal coordinates. Moreover, computed solutions of velocity and energy fields are authenticated by Durbin’s and Zakian’s Laplace inversion algorithms. The relations for skin friction and Nusselt number are evaluated in terms of velocity and temperature gradients to efficiently anticipate shear stress and rate of heat transfer at the solid–fluid interface. The respective outcomes are manifested through tables. A critical examination of the current model is carried out and repercussions of variation in implanted parameters on temperature and momentum profiles are graphically elucidated. For the sake of comparison, three limiting fractional models, named second grade, Maxwell, and viscous models, are proposed for the isothermal and ramped temperature cases. Consequently, the observed outcomes affirm that under the isothermal condition, a generalized Maxwell fluid performs the swiftest slip transport compared to other models. Inversely, a second grade fluid specifies the highest velocity profile under ramped temperature case.

这项研究的主要关注点是分析Oldroyd-B流体在振动直立板附近的广义时变磁流体动力学（MHD）滑移传输。该板在倾斜加热和非线性热辐射的作用下嵌套在多孔介质中。Caputo–Fabrizio（CF）和Atangana–Baleanu（ABC）导数用于构成分数偏微分方程，这些方程建立了滑流，切应力和热传递现象。首先，将拉普拉斯变换应用于无量纲分数模型，然后调用Stehfest的数值算法来预测主坐标中的动量和热方程的解。此外，速度和能量场的计算解决方案通过Durbin和Zakian的Laplace反演算法进行了验证。根据速度和温度梯度评估了皮肤摩擦和Nusselt数之间的关系，以有效预测固体-流体界面处的剪切应力和传热速率。各个结果通过表格显示。对当前模型进行了严格的检查，并通过图形阐明了温度和动量曲线上植入参数变化的影响。为了进行比较，针对等温和升温情况，提出了三个极限分数模型，分别称为二级，麦克斯韦和粘性模型。因此，观察到的结果证实，在等温条件下，与其他模型相比，广义的麦克斯韦流体执行了最快的滑移输送。相反，