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On some classes of almost automorphic functions and applications to fractional differential equations

✍ Scribed by G.M. Mophou; G.M. N’Guérékata


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
558 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis


We study in this paper the properties of C (n) -almost automorphic and asymptotically C (n) -almost automorphic functions (a new concept) with values in a Banach space. We then give a new result related to the existence and uniqueness of an asymptotically almost automorphic solution of a semilinear fractional differential equation of the form D α x(t) = Ax(t) + F (t, x(t), Bx(t)) with t ∈ R, 0 < α < 1, where A generates a family of α-resolvent family S α (t) and f satisfies some Lipschitz conditions.


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