Asymptotically periodic solutions of fractional differential equations
Document Type
Article
Publication Date
2-20-2013
Abstract
In three recent papers investigators have shown that a linear fractional differ- ential equation can not have a periodic solution. This raises two fundamental questions: What are the properties of the out-put function if the in-put function is periodic? What are the properties of perturbations that will leave the out-put function unchanged? We answer both questions here. The out-put function is asymptotically periodic and it is unchanged by perturbations which are L1[0,8) and by perturbations which tend to zero as t . 8 with these perturbations applied simultaneously in the damping and the forcing terms. We also find a limiting equation which this periodic function satisfies. The methods used include limiting equation techniques and fixed point methods involving both contractions and Krasnoselskii-Schaefer type. Copyright © 2013 Watam Press.
Recommended Citation
Burton, T. A. and Zhang, Bo, "Asymptotically periodic solutions of fractional differential equations" (2013). College of Health, Science, and Technology. 769.
https://digitalcommons.uncfsu.edu/college_health_science_technology/769