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<p>We introduce Bessel functions and modified Bessel functions of integer order on general time scales and establish their basic properties. The main goal is to obtain fundamental solutions of certain partial dynamic equations. Even in the purely discrete case, we obtain new formulas for the fundamental solutions of the discrete diffusion equation with backward time differences.</p>

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Bessel functions on time scales and applications to partial dynamic equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月11日

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  • Tom Cuchta,
  • Antonín Slavík

摘要

We introduce Bessel functions and modified Bessel functions of integer order on general time scales and establish their basic properties. The main goal is to obtain fundamental solutions of certain partial dynamic equations. Even in the purely discrete case, we obtain new formulas for the fundamental solutions of the discrete diffusion equation with backward time differences.