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The Cauchy problem for time-fractional linear nonlocal diffusion equations

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Abstract

This manuscript is dedicated to study the Cauchy problem for time-fractional linear nonlocal diffusion problems in the whole \({\mathbb {R}}^{N}\), including the existence and uniqueness of solutions, their asymptotic behaviour as t goes to infinity, and the analysis of the corresponding rescaled problems by rescaling the convolution kernel J in some appropriate ways. Two time-fractional models will be considered in our work, one is related to the simplest linear nonlocal diffusion operator of the form \(J*u-u\), and the other is proposed as a nonlocal analogy of higher-order evolution equations.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11471015); the Natural Science Foundation of Anhui Province (1508085MA01).

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Sen Wang & Xian-Feng Zhou

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  1. Sen Wang
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  2. Xian-Feng Zhou
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The first author SW wrote the main manuscript text and the corresponding author gave the guidance and advice. All authors reviewed the manuscript.

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Correspondence to Xian-Feng Zhou.

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Wang, S., Zhou, XF. The Cauchy problem for time-fractional linear nonlocal diffusion equations. Z. Angew. Math. Phys. 74, 156 (2023). https://doi.org/10.1007/s00033-023-02053-2

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