In this work, the flow of an electrically conducting thermoelectric micropolar fluid over a suddenly moved heated plate is considered using the methodology of fractional calculus. The governing system of coupled equations in the frame of the boundary layer equations is applied to the unsteady Stokes' first problem. Finite element technique is proposed to analyze the problem. Numerical solutions for temperature, velocity and microrotation distributions are obtained. Numerical results are computed and illustrated graphically. The effects of the flow parameters, such as fractional order, thermoelectric figure-of-merit ZT0, Seebeck coefficient k0 and magnetic parameter M on all distributions are studied with the aid of figures. The theories of coupled thermoelectric micropolar fluid and of generalized thermoelectric micropolar fluid with one relaxation time follow as a limit case. Some comparisons have been shown in figures …