New solutions of generalized MHD viscous fluid flow with thermal memory and bioconvection

In this paper, the fractional model of the bioconvection flow of a MHD viscous fluid for vertical surface has been investigated. Introducing dimensionless variables, the governing equations are solved by Laplace transform technique. Classical governing model is drawn out to fractional order technique with non-singular kernel which can be used to explain the memory for natural phenomena. Since this operator describes the rate of change at each point of the measured interval, so we use this operator. To see the behavior of related parameters physically, some graphs have been plotted in conclusion section. In the end, some useful conclusions have been attained. It is resulted that constant proportional Caputo fractional derivative measures the memory strong in comparison with Caputo and Caputo–Fabrizio fractional approaches. Further, on comparison between different kinds of viscous fluid (Water, Air, Kerosene) and found that temperature and velocity of air are higher than water and kerosene, respectively. The impacts of dimensionless numbers on velocity field have been discussed graphically and concluded that velocity increased by increasing Gr and showed opposite behavior for M and Ra .