Mellin Transform Methods for Partial Differential Equations

Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini and Gerhard Schmeisser
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Carlo Bardaro: University of Perugia, Department of Mathematics and Informatics
Paul L. Butzer: RWTH Aachen University, Lehrstuhl A für Mathematik
Ilaria Mantellini: University of Perugia, Department of Mathematics and Informatics
Gerhard Schmeisser: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Department Mathematik

Chapter Chapter 11 in Mellin Analysis, Transform Theory, and Applications, 2025, pp 301-317 from Springer

Abstract: Abstract 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 ℝ + × ℝ + . $$\mathbb {R}^+ \times \mathbb {R}^+.$$ 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.

Date: 2025
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DOI: 10.1007/978-3-031-96672-9_11

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