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Well-posedness and regularity of Caputo–Hadamard fractional stochastic differential equations

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Abstract

We prove the existence and uniqueness of the solutions to a Caputo–Hadamard fractional stochastic differential equation driven by a multiplicative white noise, which may describe the random phenomena in the ultraslow diffusion processes. The moment estimates are given in terms of the logarithmic Mittag–Leffler function. We also prove the regularity of the solutions via the logarithmic Hölder continuity.

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Acknowledgements

The authors would like to express their most sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China

    Zhiwei Yang

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xiangcheng Zheng

  3. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Hong Wang

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  1. Zhiwei Yang
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  2. Xiangcheng Zheng
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  3. Hong Wang
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Correspondence to Hong Wang.

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This work was partially funded by the ARO MURI Grant W911NF-15-1-0562, by the National Science Foundation under Grant DMS-2012291, by the National Natural Science Foundation of China under Grant 12071262, and by the China Postdoctoral Science Foundation 2021TQ0017.

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Yang, Z., Zheng, X. & Wang, H. Well-posedness and regularity of Caputo–Hadamard fractional stochastic differential equations. Z. Angew. Math. Phys. 72, 141 (2021). https://doi.org/10.1007/s00033-021-01566-y

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  • DOI: https://doi.org/10.1007/s00033-021-01566-y

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