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Paper details
Number 2 - June 2025
Volume 35 - 2025
Exact and approximate solutions of a fractional diffusion problem with fixed space memory length
Małgorzata Klimek, Tomasz Blaszczyk
Abstract
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