Almost periodic solutions of some nonlinear fractional differential equations. (English) Zbl 1201.34009

Authors’ abstract: This is a continuation of [A. Debbouche and M. M. El-Borai, Electron. J. Differ. Equ. 2009, Paper No. 46 (2009; Zbl 1171.34331)]. As in [G. N’Guérékata, Discrete Contin. Dyn. Syst. 2003, Suppl. Vol., 672–677 (2003; Zbl 1074.34056)] and [M. Bahaj and O. Sidki, Electron. J. Differ. Equ. 2002, Paper No. 98 (2002; Zbl 1026.34050)], we use the theory of fractional calculus to establish the existence and uniqueness of almost periodic solutions of a class of nonlinear fractional differential equations with analytic semigroup in a Banach space, and prove under suitable conditions that their optimal mild solutions are also weakly almost periodic.


34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
26A33 Fractional derivatives and integrals
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
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