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Mild well-posedness of equations with fractional derivative

✍ Scribed by Shangquan Bu

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
127 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study the (W^α, p^, L^p^)‐mild well‐posedness of the equation with fractional derivative D^α^u(t) = Au(t) + f(t), 0 ≤ t ≤ 2π, where A is a closed operator in a Banach space X, α > 0, 1 ≤ p < ∞ and D^α^ is the fractional derivative in the sense of Weyl. We completely characterize the (W^α, p^, L^p^)‐mild well‐posedness of this equation by L^p^‐multiplier defined by the resolvent of A, this extends the previous works by Keyantuo and Lizama.

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