Variational formulation of time-fractional parabolic equations
arXiv:1704.032576 citationsh-index: 18
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Provides rigorous theoretical foundations for fractional diffusion equations, benefiting mathematicians and modelers working on anomalous diffusion.
The paper proves well-posedness of variational formulations for time-fractional parabolic PDEs using fractional Sobolev-Bochner spaces, clarifying initial value choices.
We consider initial/boundary value problems for time-fractional parabolic PDE of order $0<α<1$ with Caputo fractional derivative (also called fractional diffusion equations in the literature). We prove well-posedness of corresponding variational formulations based entirely on fractional Sobolev-Bochner spaces, and clarify the question of possible choices of the initial value.