This article examines the effects of magnetohydrodynamics and heat absorption on an incompressible Jeffrey fluid’ time-dependent free convection flow over an infinite, vertically heated plate with homogeneous heat flux. The constitutive equation for heat flow utilizes the Prabhakar-like fractional derivative. The Laplace transform technique obtains the precise solution for the momentum and thermal profiles. The typical case and well-known outcomes from the literature are retrieved as restraining cases. The graphical analysis of the impact of the flow and fractionalized parameters on the thermal and momentum profiles is presented. Additionally, a comparison is made between the ordinary model and the Prabhakar-like fractional model, which shows that the latter better captures the retention of the physical features of the problem. It is concluded that the Prabhakar-like fractional model is better suited for describing the memory effect of the thermal and momentum fields.