On the solution existence for collocation discretizations of time-fractional subdiffusion equations
<|reference_start|>On the solution existence for collocation discretizations of time-fractional subdiffusion equations: Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness of their solutions. Two approaches are explored: the Lax-Milgram Theorem and the eigenfunction expansion. The resulting sufficient conditions, which involve certain $m\times m$ matrices (where $m$ is the order of the collocation scheme), are verified both analytically, for all $m\ge 1$ and all sets of collocation points, and computationally, for all $ m\le 20$. The semilinear case is also addressed.<|reference_end|>
@article{franz2024on,
    title={On the solution existence for collocation discretizations of
  time-fractional subdiffusion equations},
    author={Sebastian Franz, Natalia Kopteva},
    journal={arXiv preprint arXiv:2403.11847},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.11847},
    primaryClass={math.NA cs.NA}
}