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In this chapter, we first use Mellin transforms for partial differential equations of a classical type, namely variants of wave and heat equations on the wedge-shaped domain \(\mathbb {R}^+ \times \mathbb {R}^+.\) This approach seems to be very suitable for describing problems of this type. Then we apply the theory developed in Chap. 9 for studying some fractional partial differential equations.

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Mellin Transform Methods for Partial Differential Equations

  • 章节

  • 发表日期：

    2025年

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  • Carlo Bardaro,
  • Paul L. Butzer,
  • Ilaria Mantellini,
  • Gerhard Schmeisser

摘要

In this chapter, we first use Mellin transforms for partial differential equations of a classical type, namely variants of wave and heat equations on the wedge-shaped domain \(\mathbb {R}^+ \times \mathbb {R}^+.\) This approach seems to be very suitable for describing problems of this type. Then we apply the theory developed in Chap. 9 for studying some fractional partial differential equations.