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Linear subdiffusion in weighted fractional Hölder spaces

  • * Corresponding author: N. Vasylyeva

    * Corresponding author: N. Vasylyeva
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  • For $ \nu\in(0,1) $, we investigate the nonautonomous subdiffusion equation:

    $ \mathbf{D}_{t}^{\nu}u-\mathcal{L}u = f(x,t), $

    where $ \mathbf{D}_{t}^{\nu} $ is the Caputo fractional derivative and $ \mathcal{L} $ is a uniformly elliptic operator with smooth coefficients depending on time. Under suitable conditions on the given data and a minimal number (i.e. the necessary number) of compatibility conditions, the global classical solvability to the related initial-boundary value problems are established in the weighted fractional Hölder spaces.

    Mathematics Subject Classification: Primary: 35R11, 35C15; Secondary: 35B45, 26A33.


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