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Existence of positive solutions for fractional delayed evolution equations of order \(\gamma \in (1,2)\) via measure of non-compactness

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Abstract

The purpose of this paper is to consider the fractional delayed evolution equation of order \(\gamma \in (1,2)\) in ordered Banach space. In the absence of assumptions about the compactness of cosine families or related sine families, the existence results of positive solutions are studied by using some fixed point theorems and monotone iterative method under the conditions that nonlinear function satisfies the non-compactness measure conditions and some appropriate growth conditions or order conditions.

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Acknowledgements

The authors are most grateful to the editor and anonymous referees for the careful reading of the manuscript and valuable comments that helped in significantly improving an earlier version of this paper.

Funding

Q. Li is partially supported by China Postdoctoral Science Foundation (Grant No. 2020M682140), NSF of Shanxi, China (Grant No. 201901D211399).

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Authors and Affiliations

  1. School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang, 621000, People’s Republic of China

    Qiang Li & Mei Wei

  2. Department of Mathematics, Shanxi Normal University, Taiyuan, 030000, People’s Republic of China

    Jina Zhao

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  1. Qiang Li
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  2. Jina Zhao
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  3. Mei Wei
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Contributions

Q. Li completed the proof of the main results and the writing of the first draft. All authors read and approved the final manuscript.

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Correspondence to Qiang Li.

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Q. Li, M. Wei and J. Zhao declare that they have no competing interests.

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Li, Q., Zhao, J. & Wei, M. Existence of positive solutions for fractional delayed evolution equations of order \(\gamma \in (1,2)\) via measure of non-compactness. Fract Calc Appl Anal 27, 896–918 (2024). https://doi.org/10.1007/s13540-024-00248-6

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