Abstract
A new finite difference collocation algorithm has been introduced with the help of Fibonacci polynomial and then applied to one super and two sub-diffusion problems having an exact solution. It has also been shown that numerical error obtained with the investigated method is more accurate than previously existing methods. Fractional order reaction advection sub-diffusion equation containing Caputo and Riemann–Liouville fractional derivatives has been solved and the effects due to change in various parameters presented in the considered model with the graphical representation have been discussed.