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 L_{2} and L_{∞} . A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.

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