Geodesic
Weak almost periodic and optimal mild solutions of fractional evolution equations
Electronic journal of differential equations, Tome 2009 (2009)
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.
Classification : 34G10, 26A33, 35A05, 34C27, 35B15
Keywords: linear fractional evolution equation, optimal mild solution, weak almost periodicity, analytic semigroup 
@article{EJDE_2009__2009__a44,
     author = {Debbouche,  Amar and El-Borai,  Mahmoud M.},
     title = {Weak almost periodic and optimal mild solutions of fractional evolution equations},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1171.34331},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a44/}
}
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%A El-Borai,  Mahmoud M.
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%J Electronic journal of differential equations
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Debbouche,  Amar; El-Borai,  Mahmoud M. Weak almost periodic and optimal mild solutions of fractional evolution equations. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a44/