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Zbl 1194.34007
Agarwal, Ravi P.; De Andrade, Bruno; Cuevas, Claudio
On type of periodicity and ergodicity to a class of fractional order differential equations.
(English)
[J] Adv. Difference Equ. 2010, Article ID 179750, 25 p. (2010). ISSN 1687-1847/e

In this paper, the authors study some sufficient conditions for the existence and uniqueness of: a) pseudo almost periodic (in the sense of Zhang) mild solutions to some semilinear fractional differential equations, and b) asymptotically almost automorphic (in the sense of N'Guérékata) mild solutions to some semilinear fractional integro-differential equations; in all cases, the derivative $D^{\alpha}_{t}$ is considered in the sense of Riemann-Liouville with $1<\alpha<2$ and the operator $A$ is sectorial of negative type. The authors reach their goals using a theoretical operator theory approach and fixed point techniques. The results extend and complete several recent works by the authors and others (including C. Lizama, G. N'Guérékata, G. Mophou). An application to some fractional relaxation-oscillation equation is also given.
[Gaston M. N'Guerekata (Baltimore)]
MSC 2000:
*34A08
34G20 Nonlinear ODE in abstract spaces
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional differential equations; pseudo almost periodic; asymptotically almost automorphic; operator solution; mild solution; sectorial operator

Cited in: Zbl 1253.34013 Zbl 1243.34006

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