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On recent developments in the theory of boundary value problems for impulsive fractional differential equations. (English) Zbl 1268.34032
Summary: This paper is motivated from some recent papers treating the boundary value problems for impulsive fractional differential equations. We first make a counterexample to show that the formula of solutions in cited papers are incorrect. Second, we establish a general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems. Third, some sufficient conditions for the existence of the solutions are established by applying fixed point methods. Meanwhile, data dependence is obtained by using a new generalized singular Gronwall inequality. Finally, three examples are given to illustrate the results.
MSC:
34A08Fractional differential equations
34B05Linear boundary value problems for ODE
34B37Boundary value problems for ODE with impulses
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