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<p>In this paper, we examine the energy estimates and embedding properties of the fractional wave potential arising from the solution to the Cauchy problem for the time and space fractional partial differential equation. We then establish properties of the fractional wave capacity. Finally, we demonstrate some applications of these results to the wave function theory, image denoising, and signal decomposition.</p>

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Fractional Wave Potentials and Capacities with Some Applications

  • 期刊论文

  • 发表日期：

    2025年6月24日

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  • Z. Shuang,
  • J. Xiao,
  • C. Yue

摘要

In this paper, we examine the energy estimates and embedding properties of the fractional wave potential arising from the solution to the Cauchy problem for the time and space fractional partial differential equation. We then establish properties of the fractional wave capacity. Finally, we demonstrate some applications of these results to the wave function theory, image denoising, and signal decomposition.