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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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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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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DOI: https://doi.org/10.1007/s00033-023-02053-2