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.