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On piecewise continuous solutions of higher order impulsive fractional differential equations and applications

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  • Liu, Yuji

Abstract

For impulsive differential equations with fractional order, we show that the formula of solutions in cited papers are incorrect. We then give exact piecewise continuous solutions (the explicit solutions) of two classes of fractional differential equations of order α∈(n−1,n) involving Caputo derivatives and Riemann–Liouville derivatives. Apply our results to obtain existence of solutions of two classes of initial value problems of singular impulsive fractional differential equations. Examples are presented to illustrate the main theorems.

Suggested Citation

  • Liu, Yuji, 2016. "On piecewise continuous solutions of higher order impulsive fractional differential equations and applications," Applied Mathematics and Computation, Elsevier, vol. 287, pages 38-49.
    • Handle: RePEc:eee:apmaco:v:287-288:y:2016:i::p:38-49
    DOI: 10.1016/j.amc.2016.03.041
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    Cited by:

    1. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    2. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.

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