Well-posedness for an Abstract Semilinear Integro-differential Fractional Problem

Nasser eddine Tatar

doi:10.1007/s00009-010-0103-7

Well-posedness for an Abstract Semilinear Integro-differential Fractional Problem

Nasser eddine Tatar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider an abstract second order semilinear integrodifferential equation involving fractional time derivatives of order between 1 and 2. Well-posedness is established under appropriate conditions on the initial data and the nonlinearity which is itself a fractional integral. These conditions will determine the exact underlying space where to look for solutions.

Original language	English
Pages (from-to)	199-210
Number of pages	12
Journal	Mediterranean Journal of Mathematics
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s00009-010-0103-7
State	Published - Feb 2012

Bibliographical note

Funding Information:
Acknowledgement. The author is very grateful for the financial support pro-

Keywords

Cauchy problem
cosine family
fractional derivative
mildsolutions
second-order abstract problem

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-010-0103-7

Cite this

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title = "Well-posedness for an Abstract Semilinear Integro-differential Fractional Problem",

abstract = "We consider an abstract second order semilinear integrodifferential equation involving fractional time derivatives of order between 1 and 2. Well-posedness is established under appropriate conditions on the initial data and the nonlinearity which is itself a fractional integral. These conditions will determine the exact underlying space where to look for solutions.",

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AB - We consider an abstract second order semilinear integrodifferential equation involving fractional time derivatives of order between 1 and 2. Well-posedness is established under appropriate conditions on the initial data and the nonlinearity which is itself a fractional integral. These conditions will determine the exact underlying space where to look for solutions.

KW - Cauchy problem

KW - cosine family

KW - fractional derivative

KW - mildsolutions

KW - second-order abstract problem

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Well-posedness for an Abstract Semilinear Integro-differential Fractional Problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this