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Nonlocal Cauchy problems for a class of implicit impulsive fractional relaxation differential systems

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Abstract

In this paper, we discuss nonlocal Cauchy problems for a class of implicit impulsive fractional relaxation differential systems. By using vectorial version fixed point theorems and splitting the Lipschitz or linear growth conditions on the nonlinear terms into two parts and applying the techniques that use convergent to zero matrix and vector-valued norm via boundedness and continuity of Mittag-Leffler functions, two couple existence results for the solutions are presented in a complete generalized metric space or a generalized Banach space.

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Acknowledgments

This work is partially supported by Outstanding Scientific and Technological Innovation Talent Award of Education Department of Guizhou Province ([2014]240). We would also like to acknowledge the valuable suggestions from the reviewer and colleague X. Yu.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, People’s Republic of China

    Yuruo Zhang & JinRong Wang

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  1. Yuruo Zhang
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  2. JinRong Wang
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Correspondence to JinRong Wang.

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Zhang, Y., Wang, J. Nonlocal Cauchy problems for a class of implicit impulsive fractional relaxation differential systems. J. Appl. Math. Comput. 52, 323–343 (2016). https://doi.org/10.1007/s12190-015-0943-1

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  • DOI: https://doi.org/10.1007/s12190-015-0943-1

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