Amar Debbouche, Mahmoud M. El-Borai
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 , 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.
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| Amar Debbouche |
Faculty of Science, Guelma University
| Mahmoud M. El-Borai |
Faculty of Science, Alexandria University
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