Unsteady free convection flows of an incompressible differential type fluid over an infinite vertical plate with fractional thermal transport are studied. Modern definitions of the fractional derivatives in the sense of Atangana–Baleanu (ABC) and Caputo Fabrizio (CF) are used in the constitutive equations for the thermal flux. Exact solutions in both cases of the (ABC) and (CF) derivatives for the dimensionless temperature and velocity fields are established by using the Laplace transform technique. Solutions for the ordinary case and some well-known results from the literature are recovered as a limiting case. Expressions for Nusselt number and Skin friction coefficient are also determined. The influence of the pertinent parameters on temperature and velocity fields are discussed graphically. A comparison of ordinary model, and (ABC) and (CF) models are also depicted. It is found that memory of the physical aspects of the problem is well explained by fractional order (ABC) and (CF) models as compared to ordinary one. Further it is noted that the (ABC) model is the best fit to explain the memory effect of the temperature and velocity fields.

研究了具有分式热传递的无限压差型流体在无限垂直板上的非定常自由对流。热通量的本构方程使用了Atangana–Baleanu（ABC）和Caputo Fabrizio（CF）的分数导数的现代定义。使用Laplace变换技术建立了无量纲温度和速度场的（ABC）和（CF）导数的精确解。普通情况的解决方案和文献中的一些众所周知的结果被作为限制情况而得到恢复。还确定了努塞尔数和皮肤摩擦系数的表达式。讨论了有关参数对温度和速度场的影响。普通型号的比较，还描述了（ABC）和（CF）模型。已发现，与普通模型相比，分数阶（ABC）和（CF）模型可以很好地说明问题的物理方面的记忆。进一步指出，（ABC）模型最适合用来解释温度和速度场的记忆效应。