Electron. J. Diff. Equ., Vol. 2012 (2012), No. 153, pp. 1-12.

Existence of mild solutions for a neutral fractional equation with fractional nonlocal conditions

Nasser-eddine Tatar

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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