In this paper, we have considered the fractional diffusion and fractional diffusion-wave equations in which the time derivative is a fractional derivative in the Caputo form and have obtained their numerical solutions by collocation method using cubic B-spline base functions. In the solution process, for the fractional diffusion equation L1 discretizaton formula of the fractional derivative is applied, and for the fractional diffusion-wave equation L2 discretizaton formula of the fractional derivative is applied. Accuracy of the proposed method is discussed by computing the error norms L₂ and L_∞. A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.

Tbilisi Mathematical Journal, Vol. 8(2) (2015), pp. 181-193