A new mathematical model of magnetohydrodynamic (MHD) theory has
been constructed in the context of a new consideration of heat conduction with a timefractional
derivative of order 0<α≤1 and a time-fractional integral of order 0<γ≤2.
This model is applied to one-dimensional problems for a thermoelectric viscoelastic
fluid flow in the absence or presence of heat sources. Laplace transforms and statespace
techniques  will be used to obtain the general solution for any set of boundary
conditions. According to the numerical results and its graphs, conclusion about the
new theory has been constructed. Some comparisons have been shown in figures to
estimate the effects of the fractional order parameters on all the studied fields.