Abstract
A fractional scheme is proposed to solve time-fractional partial differential equations. According to the considered fractional Taylor series, the scheme is compact in space and provides fourth-order accuracy in space and second-order accuracy in fractional time. The scheme is conditionally stable when applied to the scalar fractional parabolic equation. The convergence of the scheme is demonstrated for the system of fractional parabolic equations. Moreover, a fractional model for heat and mass transfer of mixed convection flow over the flat and oscillatory plate is given. The radiation effects and chemical reactions are also considered. The scheme is tested on this model and the nonlinear fractional Burgers equation. It is found that it is more accurate than considering existing schemes in most of the regions of the solution domain. The compact scheme with exact findings of spatial derivatives is better than considering linearized equations. The error obtained by the proposed scheme with the determination of exact spatial derivatives is better than that obtained by two explicit existing schemes. The main advantage of the proposed scheme is that it is capable of providing the solution for convection-diffusion equations with compact fourth-order accuracy. Still, the corresponding implicit compact scheme is unable to find the solution to convection-diffusion problems.