Abstract
In this paper, we firstly establish an interesting impulsive Gronwall inequality with maxima involving Hadamard type singular kernel, which can be applied to make prior estimation. Secondly, we apply the above inequality and fixed point approach to show two existence results. Further, we show that finite-time stability result. Finally, an example is given to illustrate our theoretical results.
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Acknowledgments
The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too. This work is supported by the National Natural Science Foundation of China (11201091) and Outstanding Scientific and Technological Innovation Talent Award of Education Department of Guizhou Province ([2014]240).
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Zhang, Y., Wang, J. Existence and finite-time stability results for impulsive fractional differential equations with maxima. J. Appl. Math. Comput. 51, 67–79 (2016). https://doi.org/10.1007/s12190-015-0891-9
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DOI: https://doi.org/10.1007/s12190-015-0891-9