Abstract
A new mathematical model of MHD theory has been constructed in the context of a new consideration of heat conduction with a time-fractional derivative of the order alpha (0 < alpha <= 1) and a time-fractional integral of the order v (0 < v <= 2). This model is applied to MHD free convection flow of a viscous conducting fluid past an infinite surface with heat sources. Laplace transforms and state-space techniques [1] are used to obtain the general solution for any set of boundary conditions. According to the numerical results and their graphs, a conclusion about the new theory has been made. Some comparisons are shown in figures to estimate the effects of the fractional order parameters alpha, v on all studied fields for different theories.