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Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations

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Abstract

This paper first analyzes and treats the subordination principle and the approximation of fractional resolvents, extending and perfecting the theory of resolvent. Then, the approximation solvability method and the resolvent technique are developed to investigate the existence of mild solutions to a Riemann-Liouville type fractional nonlocal evolution system without the compactness condition. Moreover, effectiveness of our mentioned findings is supported by an example about a fractional diffusion system.

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Acknowledgements

The work was supported by the NSF of China (11871064,11771378) and the NSF of the JiangSu Higher Education Institutions (18KJB110019) and the Doctor Research Foundation (BT2019-03).

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Authors and Affiliations

  1. Department of Mathematics, Wuxi Institute of Technology, Wuxi, 214121, Jiangsu, People’s Republic of China

    Shouguo Zhu, Peipei Dai & Yinchun Qu

  2. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, Jiangsu, People’s Republic of China

    Gang Li

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  1. Shouguo Zhu
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  2. Peipei Dai
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  4. Gang Li
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Correspondence to Shouguo Zhu.

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Zhu, S., Dai, P., Qu, Y. et al. Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations. Fract Calc Appl Anal 26, 781–799 (2023). https://doi.org/10.1007/s13540-023-00132-9

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  • DOI: https://doi.org/10.1007/s13540-023-00132-9

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