The paper establishes well-posedness for time-fractional evolution equations in Banach spaces via a Laplace-transform solution operator, and proves uniqueness in an inverse problem of recovering the initial value.
Agmon, Lectures on Elliptic Boundary Value Problems , Van Nostrand, Princeton, 1965
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Initial boundary value problems for time-fractional evolution equations in Banach spaces
The paper establishes well-posedness for time-fractional evolution equations in Banach spaces via a Laplace-transform solution operator, and proves uniqueness in an inverse problem of recovering the initial value.