On a connection between powers of operators and fractional Cauchy problems

DOI10.1007/s00028-011-0131-1zbMath1336.47046OpenAlexW1983822773MaRDI QIDQ692823

Valentin Keyantuo, Carlos Lizama

Publication date: 6 December 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-011-0131-1

zbMATH Keywords

Cauchy problem\(C_0\)-semigroupsCaputo derivativeWright functioniterated Brownian motion\(\alpha\)-resolvent familiesPDE connectionperturbed fourth order PDEs

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) One-parameter semigroups and linear evolution equations (47D06) Fractional derivatives and integrals (26A33) Linear differential equations in abstract spaces (34G10) Transition functions, generators and resolvents (60J35) Solutions to PDEs in closed form (35C05)

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Cites Work

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• Regularized solutions for abstract Volterra equations
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• Brownian subordinators and fractional Cauchy problems
• On Subordinated Holomorphic Semigroups
• One-Parameter Semigroups for Linear Evolution Equations
• Schauder estimates for equationswith fractional derivatives
• Higher order PDE’s and iterated processes
• THE GENERALIZED BESSEL FUNCTION OF ORDER GREATER THAN ONE
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