Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 46, pp. 1-8.

Title: Weak almost periodic and optimal mild solutions
       of fractional evolution equations
   
Authors: Amar Debbouche  (Guelma Univ., Guelma, Algeria)
         Mahmoud M. El-Borai (Alexandria Univ., Alexandria, Egypt)

Abstract:
 In this article, we prove the existence of optimal mild
 solutions for linear fractional evolution equations with
 an analytic semigroup in a Banach space. As in [16], we use
 the Gelfand-Shilov principle to prove existence, and
 then the Bochner almost periodicity condition to show 
 that solutions are weakly almost periodic.
 As an application, we study a fractional partial differential
 equation of parabolic type. 
 
Submitted March 10, 2009. Published March 30, 2009.
Math Subject Classifications: 34G10, 26A33, 35A05, 34C27, 35B15. 
Key Words: Linear fractional evolution equation;
           Optimal mild solution; weak almost periodicity; 
	   analytic semigroup.