Study of transition times in diffusion processes using fractional order derivatives
DOI:
https://doi.org/10.15407/fmmit2025.41.103Keywords:
mathematical modeling, fractional calculus, diffusion processes, methods for solving boundary value problems, methods of complex variable function theoryAbstract
The paper develops a mathematical model of the diffusion process using Caputo fractional-order derivatives with
respect to time. The problem solution was obtained in an analytical form through contour integration methods. An
analytical solution provides explicit expressions for the diffusion behavior across the entire time range, including
both short- and long-time ranges. The emphasis on analytical solutions arises from the sensitivity of fractionalorder
models to variations in the derivative order, and the implementation of numerical methods does not always
allow for reducing the discretization step. Literature analysis indicates that even slight changes in the fractional
derivative order can lead to significant differences in results. Therefore, it is crucial to obtain the results in an
analytical form that will allow us to adapt and optimize them in relation to real information about the process
being modeled.
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