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Mild well‐posedness of equations with fractional derivative
Author(s) -
Bu Shangquan
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000056
Subject(s) - mathematics , fractional calculus , derivative (finance) , multiplier (economics) , resolvent , banach space , operator (biology) , pure mathematics , mathematical analysis , mathematical physics , biochemistry , chemistry , repressor , gene , transcription factor , financial economics , economics , macroeconomics
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.