YANG Xu-jun, SONG Qian-kun. On the Existence of Anti-Periodic Solutions in Time-Invariant Fractional Order Systems[J]. Applied Mathematics and Mechanics, 2014, 35(6): 684-691. doi: 10.3879/j.issn.1000-0887.2014.06.010
Citation: YANG Xu-jun, SONG Qian-kun. On the Existence of Anti-Periodic Solutions in Time-Invariant Fractional Order Systems[J]. Applied Mathematics and Mechanics, 2014, 35(6): 684-691. doi: 10.3879/j.issn.1000-0887.2014.06.010

On the Existence of Anti-Periodic Solutions in Time-Invariant Fractional Order Systems

doi: 10.3879/j.issn.1000-0887.2014.06.010
Funds:  The National Natural Science Foundation of China(61273021)
  • Received Date: 2014-03-24
  • Rev Recd Date: 2014-05-06
  • Publish Date: 2014-06-11
  • The anti-periodic solution problem makes an important characteristic of dynamics for nonlinear differential systems. In recent years, the anti-periodic solution problem in integer order nonlinear differential systems had been widely studied, while the anti-periodic solution problem in fractional order nonlinear differential systems had been preliminarily discussed. Other than the previous work, the existence of anti-periodic solutions in time-invariant fractional order systems was investigated. It is shown that although within a finite time interval the solutions do not show any anti-periodic behavior, when the lower limit of the fractional order derivative tends to infinity the anti-periodic orbits will be obtained.
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