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    A Galerkin Finite Element Method to Solve Fractional Diffusion and Fractional Diffusion-Wave Equations
    (Vilnius Gediminas Tech Univ, 2013) Esen, Alaattin; Ucar, Yusuf; Yagmurlu, Nuri; Tasbozan, Orkun
    In 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.