Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

被引：2
|
作者：
Tatar, Nasser-eddine [1 ]
机构：
[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2011年
关键词：
Cauchy problem; Cosine family; Fractional derivative; Mild solutions; Neutral second-order abstract problem; BEAM; EQUATION;
D O I：
10.1186/1687-1847-2011-18
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order case to the fractional case in the sense of Caputo. A fixed point theorem is used to prove existence of mild solutions.
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页数：12
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