Abstract
A second-order abstract problem with derivatives of non-integer order is investigated. The nonlinearity involves fractional derivatives between 1 and 2. Existence and uniqueness of mild and classical solutions are established in appropriate spaces. This work extends similar works with or without a derivative of first order and also a work of the present author, where the order of the derivatives were between 0 and 1.
| Original language | English |
|---|---|
| Pages (from-to) | 53-65 |
| Number of pages | 13 |
| Journal | Mathematical Modelling and Analysis |
| Volume | 18 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2013 |
Bibliographical note
Funding Information:The author is very grateful for the financial support provided by King Fahd University of Petroleum and Minerals through project No. IN 100007.
Keywords
- Cauchy problem
- cosine family
- fractional derivative
- mild solutions
- second-order abstract problem
ASJC Scopus subject areas
- Analysis
- Modeling and Simulation
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