Abstract
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.
| Original language | English |
|---|---|
| Article number | 18 |
| Journal | Advances in Difference Equations |
| Volume | 2011 |
| DOIs | |
| State | Published - 2011 |
Bibliographical note
Funding Information:The author is very grateful for the financial support provided by King Fahd University of Petroleum and Minerals through the project No. IN 100007.
Keywords
- Cauchy problem
- Cosine family
- Fractional derivative
- Mild solutions
- Neutral second-order abstract problem
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics
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