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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 1364532, 12 pages
Research Article

Periodic Solutions and -Asymptotically Periodic Solutions to Fractional Evolution Equations

Jia Mu,1,2 Yong Zhou,1,3 and Li Peng1

1Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
2School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, Gansu 730000, China
3Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Correspondence should be addressed to Yong Zhou

Received 1 January 2017; Accepted 15 March 2017; Published 3 April 2017

Academic Editor: Can Li

Copyright © 2017 Jia Mu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the existence and uniqueness of periodic solutions, -asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.