Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative towards an oscillating tensile plate are discussed in this paper. The fractional operator is introduced to material derivative for the first time to obtain a newly defined constitutive equation of Maxwell fluid. The Fourier's law is modified accordingly. The pressure gradient is innovatively obtained by solving the differential equation, which bases on the momentum equation away from the plate. Furthermore, the numerical solutions are acquired by virtue of the finite difference method combined with L1-algorithm. It turns out to be convergent through constructing numerical example. The influence of related parameters on the velocity and temperature are performed graphically in detail. Results show that the fluid velocity and temperature distributions tend to periodic oscillation near the plate. Both the velocity and the temperature reduce with the augment of fractional derivative parameters, which indicates the velocity and the temperature boundary layer become thinner. The smaller velocity relaxation time parameter leads to enhanced velocity, meaning that the pressure promotes the fluid velocity. It is evident that all the temperature curves have a tendency to increase first and then decrease with the diverse parameters due to the thermal relaxation characteristic.

本文讨论了具有对流导数的分数麦克斯韦流体向振荡张拉板的非定常斜驻点流动和传热。首次将分数算子引入材料导数，得到新定义的麦克斯韦流体本构方程。傅立叶定律相应地进行了修改。压力梯度创新性地通过求解微分方程得到，该微分方程基于远离板的动量方程。此外，利用有限差分法结合L1算法获得数值解。通过构造数值例子证明是收敛的。相关参数对速度和温度的影响以图形方式详细进行。结果表明，在板块附近，流体速度和温度分布趋于周期性振荡。随着分数阶导数参数的增大，速度和温度均降低，这表明速度和温度边界层变薄。较小的速度弛豫时间参数会导致速度增加，这意味着压力会促进流体速度。很明显，由于热弛豫特性，所有温度曲线都具有随着参数的变化先升高后降低的趋势。较小的速度弛豫时间参数会导致速度增加，这意味着压力会促进流体速度。很明显，由于热弛豫特性，所有温度曲线都具有随着参数的变化先升高后降低的趋势。较小的速度弛豫时间参数会导致速度增加，这意味着压力会促进流体速度。很明显，由于热弛豫特性，所有温度曲线都具有随着参数的变化先升高后降低的趋势。