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A study on impulsive fractional hybrid evolution equations using sequence method

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Abstract

In this paper, we introduce a new concept called \(\alpha \)-order cosine-resolvent family, by using the theory of fractional calculus, the concepts of measure of noncompactness and Hybrid fixed point theorem, we consider the existence of PC-mild solutions for a class of impulsive fractional hybrid evolution equation in a Banach space . Furthermore, we obtain some sufficient conditions for approximate controllability of our concern problem. At the end, an example is given to illustrate the feasibility of our results.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Haide Gou & Yongxiang Li

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  1. Haide Gou
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  2. Yongxiang Li
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Correspondence to Haide Gou.

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Communicated by José Tenreiro Machado.

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Supported by the National Natural Science Foundation of China (Grant no. 11661071).

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Gou, H., Li, Y. A study on impulsive fractional hybrid evolution equations using sequence method. Comp. Appl. Math. 39, 225 (2020). https://doi.org/10.1007/s40314-020-01239-y

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  • DOI: https://doi.org/10.1007/s40314-020-01239-y

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