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
• DOI: 10.1016/j.camwa.2009.05.008

✦ 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.