Numerical Study for Fractional-Order Magnetohydrodynamic Boundary Layer Fluid Flow Over Stretching Sheet

Abstract

In this letter, the MHD boundary layer fluid flow of nonNewtonian power-law on a stretching plate in the presence of a magnetic field has been investigated. The deductive group-theoretic technique is utilized to transform the proposed mathematical problem into a non-linear ODE. The solution of the converted differential equation is studied via the quartic B-spline method and the modified Laplace decomposition method. The approximate solutions are explained through tables and illustrative graphs for different values of the fractional order derivatives implementing the modified Laplace decomposition technique. We have used the Caputo sense of fractional derivative in this paper. A comparison of the obtained results reveals that both techniques are effective and reliable tools for the solutions of boundary value problems in fluid flow. It is found that when the pate and the fluid move in the same direction, the velocity profile declines and then improves at the end of the trend while the velocity profile gradually increases when the pate is stationary. The effect of the fractional order derivative on the velocity profile is another novelty of the present work. Furthermore, the influence of the physical parameters and the fractional order derivative on the stream function and the velocity profile is shown via tables and illustrative graphs.