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

被引：1

作者：

Tatar, Nasser-eddine ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2012年 / 9卷 / 01期

关键词：

Cauchy problem; cosine family; fractional derivative; mild solutions; second-order abstract problem;

D O I：

10.1007/s00009-010-0103-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：199 / 210

页数：12

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