Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 153, pp. 1-12.

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

Author: Nasser-eddine Tatar (King Fahd Univ. Dhahran, Saudi Arabia)

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 07, 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.