Well-posedness for an abstract semilinear integro-differential fractional problem

DOI10.1007/S00009-010-0103-7zbMath1241.45008OpenAlexW1987215667MaRDI QIDQ414399

Nasser-eddine Tatar

Publication date: 11 May 2012

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-010-0103-7

zbMATH Keywords

Cauchy problemmild solutionsfractional derivativecosine familysecond-order abstract problem

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Second-order nonlinear hyperbolic equations (35L70) Second-order hyperbolic equations (35L10) Abstract hyperbolic equations (35L90) Fractional partial differential equations (35R11)

Related Items (1)

Mild solution of second-order impulsive integro-differential evolution equations of Volterra type in Banach spaces

Cites Work

• Remarks on the existence results for second-order differential inclusions with nonlocal conditions
• Existence of solutions for second order partial neutral functional differential equations
• Abel integral equations. Analysis and applications
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Theorem about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a banach space
• Cosine families and abstract nonlinear second order differential equations
• An Abstract Second Order Semilinear Volterra Integrodifferential Equation
• Existence of mild solutions of second order initial value problems for delay integrodifferential inclusions with nonlocal conditions
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