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On the concept and existence of solution for impulsive fractional differential equations. (English) Zbl 1252.35277
Summary: This paper is motivated from some recent papers treating the problem of the existence of a solution for impulsive differential equations with fractional derivative. We firstly show that the formula of solutions in cited papers are incorrect. Secondly, we reconsider a class of impulsive fractional differential equations and introduce a correct formula of solutions for a impulsive Cauchy problem with Caputo fractional derivative. Further, some sufficient conditions for existence of the solutions are established by applying fixed point methods. Some examples are given to illustrate the results.
MSC:
35R12Impulsive partial differential equations
35R11Fractional partial differential equations
35A01Existence problems for PDE: global existence, local existence, non-existence
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