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1 International Journal of Applied Mathematics and Computer Science

1 2025

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Exact and approximate solutions of a fractional diffusion problem with fixed space memory length

Klimek Malgorzata, Blaszczyk Tomasz

International Journal of Applied Mathematics and Computer Science

2025

Vol. 35, no. 2

311--328

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.