Application of fractal fractional derivative of power law kernel (FFP0Dxα,ß) to MHD viscous fluid flow between two plates

In this problem, I have studied the application of newly introduced fractal fractional operators with power law kernel in fluid dynamics. We Considered the MHD viscous fluid flow between two plates such that the upper plate is in motion with constant velocity while the lower plate is at rest. The governing equation developed from the problem can be formulated withe fractal fractional derivative operator with power law kernel. The proposed fractal fractional model can be solved by means of Laplace transform technique and obtained exact solutions. To see the impact of magnetic field M, fractional alpha as well as fractal parameter beta on the fluid velocity field, we plotted some graphs through MathCad software and presented in the graphical section. As a result, we found that for larger values of alpha and beta, a decay in velocity of the fluid was observed. Further, fractal fractional model more slow down the velocity of the model in comparison of fractional only. Therefore, a combined approach of fractal fractional explains the memory of the function better than fractional only. (C) 2020 Elsevier Ltd. All rights reserved.