Abstract
In this study, an attempt is made to investigate a fractional model of unsteady and an incompressible MHD viscous fluid with heat transfer. The fluid is lying over a vertical and moving plate in its own plane. The problem is modeled by using the constant proportional Caputo fractional derivatives with suitable boundary conditions. The non-dimensional governing equations of problem have been solved analytically with the help of Laplace transform techniques and explicit expressions for respective field variable are obtained. The transformed solutions for energy and momentum balances are appeared in terms of series form. The analytical results regarding velocity and temperature are plotted graphically by MATHCAD software to see the influence of physical parameters. Some graphic comparisons are also mad among present results with hybrid fractional derivatives and the published results that have been obtained by Caputo. It is found that the velocity and temperature with constant proportional Caputo fractional derivative are portrait better decay than velocities and temperatures that obtained with Caputo and Caputo-Fabrizio derivative. Further, rate of heat transfer and skin friction can be enhanced with smaller values of fractional parameter.