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General methods for converting impulsive fractional differential equations to integral equations and applications

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  • Yuji Liu

Abstract

In this paper, we propose the concepts of Caputo fractional derivatives and Caputo type Hadamard fractional derivatives for piecewise continuous functions. We obtain general solutions of four classes of impulsive fractional differential equations (Theorem 3.1–Theorem 3.4) respectively. These results are applied to converting boundary value problems for impulsive fractional differential equations to integral equations. Some comments are made on recently published papers (see Section 4).

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  • Yuji Liu, 2018. "General methods for converting impulsive fractional differential equations to integral equations and applications," Mathematische Nachrichten, Wiley Blackwell, vol. 291(2-3), pages 443-491, February.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:2-3:p:443-491
    DOI: 10.1002/mana.201600318
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