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-infinity. A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.
C1 [Esen, A.; Tasbozan, O.; Ucar, Y.; Yagmurlu, N. M.] Inonu Univ, Fac Art & Sci, Dept Math, TR-44280 Malatya, Turkey.