Mild well‐posedness of equations with fractional derivative | Zendy

Bu Shangquan | Zendy

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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.

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