Mild well-posedness of equations with fractional derivative

DOI10.1002/mana.201000056zbMath1251.47013OpenAlexW2070628511MaRDI QIDQ3118972

Shang Quan Bu

Publication date: 6 March 2012

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201000056

zbMATH Keywords

fractional Sobolev spacesfractional derivative\((W^{\alpha,p}\(L^{p}\)-Fourier multipliersL^{p})\)-mild well-posedness

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Fractional derivatives and integrals (26A33) Equations and inequalities involving linear operators, with vector unknowns (47A50) Linear differential equations in abstract spaces (34G10) Multipliers in one variable harmonic analysis (42A45)

Related Items (9)

Maximal regularity in \(l_{p}\) spaces for discrete time fractional shifted equations ⋮ On the well-posedness of degenerate fractional differential equations in vector valued function spaces ⋮ lp-maximal regularity for fractional difference equations on UMD spaces ⋮ Existence and uniqueness of solutions for a class of discrete-time fractional equations of order \(2<\alpha \leq 3\) ⋮ Strongly \(L^p\) well-posedness for abstract time-fractional Moore-Gibson-Thompson type equations ⋮ Lebesgue regularity for nonlocal time-discrete equations with delays ⋮ Asymptotic behavior of mild solutions to fractional Cauchy problems in Banach spaces ⋮ Mild solutions to integro-differential equations in Banach spaces ⋮ Well posedness for semidiscrete fractional Cauchy problems with finite delay

Cites Work

• Unnamed Item
• The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
• Mild well-posedness of vector-valued problems on the real line
• Well-posedness of equations with fractional derivative
• Operator-valued Fourier multipliers on periodic Triebel spaces
• A characterization of periodic solutions for time-fractional differential equations in UMD spaces and applications
• OPERATOR-VALUED FOURIER MULTIPLIERS ON PERIODIC BESOV SPACES AND APPLICATIONS
• Periodic L 2 -Solutions of an Integrodifferential Equation in a Hilbert Space
• Schauder estimates for equationswith fractional derivatives

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