Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations
Joint Authors
Huang, Zaitang
Cao, Junfei
N'Guérékata, Gaston M.
Source
International Journal of Differential Equations
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-08-01
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
This paper is concerned with the existence of asymptotically almost automorphic mild solutions to a class of abstract semilinear fractional differential equations D t α x t = A x t + D t α - 1 F t , x t , B x t , t ∈ R , where 1 < α < 2 , A is a linear densely defined operator of sectorial type on a complex Banach space X and B is a bounded linear operator defined on X , F is an appropriate function defined on phase space, and the fractional derivative is understood in the Riemann-Liouville sense.
Combining the fixed point theorem due to Krasnoselskii and a decomposition technique, we prove the existence of asymptotically almost automorphic mild solutions to such problems.
Our results generalize and improve some previous results since the (locally) Lipschitz continuity on the nonlinearity F is not required.
The results obtained are utilized to study the existence of asymptotically almost automorphic mild solutions to a fractional relaxation-oscillation equation.
American Psychological Association (APA)
Cao, Junfei& Huang, Zaitang& N'Guérékata, Gaston M.. 2018. Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations. International Journal of Differential Equations،Vol. 2018, no. 2018, pp.1-23.
https://search.emarefa.net/detail/BIM-1170826
Modern Language Association (MLA)
Cao, Junfei…[et al.]. Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations. International Journal of Differential Equations No. 2018 (2018), pp.1-23.
https://search.emarefa.net/detail/BIM-1170826
American Medical Association (AMA)
Cao, Junfei& Huang, Zaitang& N'Guérékata, Gaston M.. Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations. International Journal of Differential Equations. 2018. Vol. 2018, no. 2018, pp.1-23.
https://search.emarefa.net/detail/BIM-1170826
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1170826