Time-fractional diffusion equation in the fractional Sobolev spaces

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Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, methodology): “Eidelman and Kochubei [21] derived fundamental solutions to problem in the whole space using Fox H-functions, and derived various estimates, see also [92, 29];.”
A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition (2018, unknown): “4 and (24) in (23), we get |τ|α|ûεn(τ)|2 ≤ C max{1, |τ|α−1}||ûεn(τ)||H1(Ω).”
Weyl and Marchaud Derivatives: A Forgotten History (2017, background): “This last remark is essentially based on the popularity of other fractional derivatives, for instance the Riemann-Liouville derivative or the Caputo derivative, see [39], [33] and [29], for a modern approach to these operators.”
Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations (2016, background): “Following the same line as that in [7], we shall redefine the weak solution to (1.”
Well-posedness of general Caputo-type fractional differential equations (2018, background): “In [7], the authors suggested a new definition of the Caputo fractional derivative in the fractional Sobolev space and proved the maximal regularity of solutions of time-fractional diffusion equations involving the Caputo derivative.”