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Piecewise weighted pseudo almost periodicity of impulsive integro-differential equations with fractional order \(1<\alpha <2\)

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Abstract

We give the existence theorem of piecewise weighted pseudo almost periodic mild solutions for impulsive integro-differential equations with fractional order \(1<\alpha <2\), where A is a linear closed and densely defined operator of sectorial type in a complex Banach space \({{\mathbb {X}}}\). The main results are obtained by Banach contraction mapping principle. An example is given to illustrate the main results.

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Acknowledgements

This work is supported by a Grant of NNSF of China (nos. 11471227, 11561077) and Scientific Research Fund of Sichuan Provincial Education Department (no. 18ZB0512).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University of Arts and Science, Dazhou, 635000, Sichuan, People’s Republic of China

    Chuan-Yun Gu

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Hong-Xu Li

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  1. Chuan-Yun Gu
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  2. Hong-Xu Li
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Correspondence to Hong-Xu Li.

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Communicated by Juan Seoane Sepúlveda.

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Gu, CY., Li, HX. Piecewise weighted pseudo almost periodicity of impulsive integro-differential equations with fractional order \(1<\alpha <2\). Banach J. Math. Anal. 14, 487–502 (2020). https://doi.org/10.1007/s43037-019-00004-6

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  • DOI: https://doi.org/10.1007/s43037-019-00004-6

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