Esen, A.Tasbozan, O.Ucar, Y.Yagmurlu, N. M.2024-08-042024-08-0420151875-158X1512-0139https://doi.org/10.1515/tmj-2015-0020https://hdl.handle.net/11616/102162In 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.eninfo:eu-repo/semantics/openAccessFinite element methodCollocation methodFractional diffusion equationFractional diffusion-wave equationCubic B-splineArticle8218119310.1515/tmj-2015-0020WOS:000219434000016N/A