Exact Analysis of Fractionalised Jeffrey Fluid in a Channel with Caputo and Caputo Fabrizio Time Derivative: A Comparative Study

Abstract The non-integer order derivatives, Caputo (C) and Caputo Fabrizio (CF), were employed to analyse the natural convective flow of magnetohydrodynamic (MHD) Jeffrey fluid. The aim is to generalise the idea of Jeffrey’s fluid flow. The fluid flow is elaborated between two vertical parallel plates. One plate is kept fixed while the other is moving with the velocity U0f(t), which induces the motion in the fluid. The fluid flow problem is modelled in terms of the partial differential equation along with generalised physical conditions. The appropriate parameters are introduced to the dimensionless system of equations. To obtain the solutions, the Laplace transform (LT) is operated on the fractional system of equations, and the results are presented in series form. The pertinent parameter’s influence on the fluid flow is brought under consideration to reveal interesting results. In comparison, we noticed that the C approach shows better results than CF, and graphs are drawn to show the results. The results for ordinary Jeffrey fluid, second-grade and viscous fluid are obtained in a limiting sense.