Approximation of Caputo-Prabhakar derivative with application in solving time fractional advection-diffusion equation

This work aims to numerically approximate the Caputo-Prabhakar derivative and use this approximation for solving the time-fractional advection-diffusion equation defined in Caputo-Prabhakar sense which is widely used in fluid dynamics. In this approach, we approximate the time-fractional derivative of the mentioned equation by two schemes, namely NS1 and NS2, using linear and quadratic interpolation functions, respectively. The convergence order of the two schemes is 2-alpha, 3-alpha, respectively, for 0更多