Exact and approximate solutions of a fractional diffusion problem with fixed space memory length - Klimek, Małgorzata; Blaszczyk, Tomasz (Zielona Góra: Uniwersytet Zielonogórski)
We study a fractional differential diffusion equation, where the spatial derivative is expressed by the fractional differential operator with a fixed space memory length. The exact solution of the considered problem is presented, taking into account the homogeneous Dirichlet boundary conditions. Additionally, since the solution is in the form of a trigonometric series, we also present approximate solutions in the form of the truncated series. The accuracy of the approximation is controlled by the derived bound of a approximation error.
Keywords: fractional diffusion problem; series solution; error estimation; fixed memory length