<p>The study examines the natural convection flow of viscous electrically conductive fluid between two vertical plates in time-dependent thermal conditions with magnetohydrodynamics effect. A fractional-order model that is a generalization of the classical Fourier law by using the Caputo-Fabrizio fractional integral is developed. The model equations are rewritten in analytical form using a synthesis of the Laplace techniques and sine-based Fourier analysis to get analytical solutions. The latter expressions are modeled in generalized G-functions that are useful in generalizing the impact of fractional dynamics. Mathcad is used to assess the analytical results and contour plots in 2Ds are used to illustrate the temperature distribution of the fluid domain at various levels of time. The influence of critical physical determinants, including the fractional order, the intensity of the magnetic field, the Grashof number, and the term associated with heat source/sink, is analyzed comprehensively. The results suggest that elevated values of the fractional parameter enhance both heat retention and fluid velocity due to the phenomenon known as the memory effect.</p>