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| A LYAPUNOV-TYPE INEQUALITY FOR A PERIODIC BOUNDARY VALUE PROBLEM OF A FRACTIONAL DIFFERENTIAL EQUATION |
| Xing Zhu,Yuqiang Feng,Yuanyuan Wang |
| (College of Science, Wuhan University of Science and Technology, Wuhan 430065, Hubei, PR China; Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, Hubei, PR China) |
| DOI： |
| Abstract: |
| In this paper, we establish a Lyapunov-type inequality for fractional differential periodic boundary-value problems. As applications, a necessary condition is obtained to ensure the existence and uniqueness of nontrivial solutions to this problem. |
| Key words: fractional differential equation; periodic boundary condition; Lyapunov-type inequality; Mittag-Leffler functions |