Exact and Approximate Solutions of A Fractional Diffusion Problem with Fixed Space Memory Length

Klimek, Malgorzata; Blaszczyk, Tomasz

doi:10.61822/amcs-2025-0022

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.

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Exact and Approximate Solutions of A Fractional Diffusion Problem with Fixed Space Memory Length

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