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

El-Borai, Mahmoud M.; Debbouche, Amar

Int. J. Contemp. Math. Sci. 4, No. 25-28, 1373-1387 (2009).

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.

Reviewer: Li Changpin (Logan)

MSC:

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

Keywords:

nonlinear parabolic equation with fractional order; almost periodic solution; optimal mild solution; weak almost periodicity; analytic semigroup

Citations:

Zbl 1171.34331; Zbl 1074.34056; Zbl 1026.34050