Convergence analysis and approximation solution for the coupled fractional convection-diffusion equations

By using maximum principle approach, the existence, uniqueness and stability of a coupled fractional partial differential equations is studied. A new fractional characteristic finite difference scheme is given for solving the coupled system. This method is based on shifted Grunwald approximation and Diethelm's algorithm. We obtain the optimal convergence rate for this scheme and drive the stability estimates. The results are justified by implementing an example of the fractional order time and space dependent in concept of the complex Levy motion. Also, the numerical results are examined for disinfection and sterilization of tetanus. (C) 2016 All rights reserved.