
Sharp pointwiseintime error estimate of L1 scheme for nonlinear subdiffusion equations
An essential feature of the subdiffusion equations with the αorder time...
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Estimates on translations and Taylor expansions in fractional Sobolev spaces
In this paper we study how the (normalised) Gagliardo seminorms [u]_W^s...
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Regularization of backward timefractional parabolic equations by Sobolev equations methods
It is wellknown that backward parabolic equations in which the initial ...
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Time fractional gradient flows: Theory and numerics
We develop the theory of fractional gradient flows: an evolution aimed a...
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Timeadaptive optimization in a parameter identification problem of HIV infection
The paper considers a timeadaptive method for determination of drug eff...
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Error analysis for timefractional semilinear parabolic equations using upper and lower solutions
A semilinear initialboundary value problem with a Caputo time derivativ...
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A Caputo fractional derivativebased algorithm for optimization
We propose a novel Caputo fractional derivativebased optimization algor...
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Pointwiseintime a posteriori error control for timefractional parabolic equations
For timefractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwiseintime a posteriori error bounds in the spatial L_2 and L_∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2α in the presence of solution singularities.
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