King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran 31261, Saudi Arabia
email: tatarn@kfupm.edu.sa
Nasser-eddine Tatar
Abstract:
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.
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Nasser-eddine Tatar King Fahd University of Petroleum and Minerals Department of Mathematics and Statistics Dhahran 31261, Saudi Arabia email: tatarn@kfupm.edu.sa |
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