The existence of mild solutions in an appropriate space is established for a second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the initial conditions. We introduce some new spaces taking into account the minimum requirements of regularity.
Submitted May 5, 2012. Published September 7, 2012.
Math Subject Classifications: 26A33, 34K40, 35L90, 35L70, 35L15, 35L07.
Key Words: Cauchy problem; cosine family; fractional derivative; mild solutions; neutral second-order abstract problem.
Show me the PDF file (228 KB), TEX file, and other files for this article.
| Nasser-eddine Tatar |
King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran 31261, Saudi Arabia
Return to the EJDE web page