Application of cubic B-spline quasi-interpolation for solving timefractional partial differential equation

The purpose of this paper is to present a numerical scheme for solving time-fractional partial differential equation based on cubic B-spline quasi-interpolation. For this purpose, first we will approximate the time-fractional derivative by Laplace transform method and then by using of cubic B-spline quasi-interpolation, the spatial derivatives are approximated. Moreover, the stability of this method is studied. Finally, European call and put options are priced and we will show that the results are good agreement with the other methods. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement.