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arXiv · 2402.03482

On time-fractional partial differential equations of time-dependent piecewise constant order

Yavar Kian·Marián Slodička·Éric Soccorsi·Karel Van Bockstal
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Abstract

This contribution considers the time-fractional subdiffusion with a time-dependent variable-order fractional operator of order $\beta(t)$. It is assumed that $\beta(t)$ is a piecewise constant function with a finite number of jumps. A proof technique based on the Fourier method and results from constant-order fractional subdiffusion equations has been designed. This novel approach results in the well-posedness of the problem.

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Yavar Kian, Marián Slodička, Éric Soccorsi, Karel Van Bockstal. 2024-02-05. On time-fractional partial differential equations of time-dependent piecewise constant order. https://doi.org/10.1002/mma.10439

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