This paper examines the transient motion of a viscous and incompressible fluid between two infinite vertical parallel plates due to natural convection current occurring as a result of application of isothermal conditions on the plates. Laplace transform method is used to solve the partial differential equation governing the problem while a numerical algorithm based on Riemann-Sum approximation is used to transform the solution from Laplace domain to time domain. The classical model of transient natural convection flow is extended to some fractional models; precisely, Caputo-Fabrizio (C.F) and Atangana-Baleanu (ABC). We obtained semi analytical results for temperature, Nusselt number, velocity and shear stress through MATLAB software. In this regards, we have noticed that both fractional models; C.F and ABC give more generalized results relative to the classical case.