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

Yuji Liu

Mathematische Nachrichten, 2018, vol. 291, issue 2-3, 443-491

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).

Date: 2018
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