The unsteady flow of Jeffrey fluid along with a vertical plate is studied in this paper. The equations of momentum, energy, and generalized Fourier’s law of thermal flux are transformed to non-dimensional form for the proper dimensionless parameters. The Prabhakar fractional operator is applied to acquire the fractional model using the constitutive equations. To obtain the generalized results for velocity and temperature distribution, Laplace transform is performed. The influences of fractional parameters , thermal Grashof number , and non-dimensional Prandtl number upon velocity and temperature distribution are presented graphically. The results are improved in the form of decay of energy and momentum equations, respectively. The new fractional parameter contains the Mittag-Leffler kernel with three fractional parameters which are responsible for better memory of the fluid properties rather than the exponential kernel appearing in the Caputo–Fabrizio fractional operator. The Prabhakar fractional operator has advantage over Caputo–Fabrizio in the real data fitting where needed.

中文翻译：

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无限板上具有傅立叶定律的杰弗里流体的广义热通量流动

本文研究了杰弗里流体沿垂直板的非定常流动。对于适当的无量纲参数，动量方程、能量方程和广义傅立叶热通量定律被转换为无量纲形式。应用 Prabhakar 分数运算符来获取使用本构方程的分数模型。为了获得速度和温度分布的广义结果，执行拉普拉斯变换。分数参数的影响，热格拉斯霍夫数，和无量纲普朗特数时的速度和温度分布图形呈现。结果分别以能量和动量方程的衰减形式得到改进。新的分数参数包含具有三个分数参数的 Mittag-Leffler 内核，这些参数负责更好地记忆流体特性，而不是出现在 Caputo-Fabrizio 分数运算符中的指数内核。在需要的实际数据拟合中，Prabhakar 分数运算符比 Caputo-Fabrizio 具有优势。