Analysis of MHD viscous fluid flow through porous medium with novel power law fractional differential operator

Abstract

The present study deals with the unsteady and incompressible viscous fluid flow with constant proportional Caputo type fractional derivative (hybrid fractional operator). We find analytical solutions of a well-known problem in fluid dynamics known as Stokes’ first problem. MHD and porosity are also considered as an additional effects. Using dimensional analysis, governing equations of motion converted into non-dimensional form and then extended with novel fractional operator of singular kernel and series solutions are obtained by Laplace transform method. As a result, we compared present result with all the existing fractional operators and found that momentum boundary layer thickness can be control by changing the value of fractional parameter. Moreover, it is also observed that constant proportional Caputo type operator is well suited in exhibiting the decay of velocity of the fluid than all the existing fractional operators with power law (C), exponential law (CF) and Mittage-Leffler law (ABC).