Esen, AlaattinUcar, YusufYagmurlu, NuriTasbozan, Orkun2024-08-042024-08-0420131392-62921648-3510https://doi.org/10.3846/13926292.2013.783884https://hdl.handle.net/11616/96010In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L2 and L1 are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.eninfo:eu-repo/semantics/openAccessfinite element methodGalerkin methodfractional diffusion equationfractional diffusion-wave equationquadratic B-splineArticle18226027310.3846/13926292.2013.7838842-s2.0-84876308850Q3WOS:000318165900008Q3