Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics (MHD) flows. The time derivative is expressed by means of Caputo's fractional derivative concept, while the model is solved via the full-spectral method (FSM) and the semi-spectral scheme (SSS). The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques. The SSS is developed by discretizing the time variable, and the space domain is collocated by using equal points. A detailed comparative analysis is made through graphs for various parameters and tables with existing literature. The contour graphs are made to show the behaviors of the velocity and magnetic fields. The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows, and the concept may be extended for variable order models arising in MHD flows.