A generalisation of the Malgrange-Ehrenpreis theorem to find fundamental solutions to fractional PDEs

作者：Baleanu Dumitru; Fernandez Arran^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2017, (15): 1-12.

DOI：10.14232/ejqtde.2017.1.15

• fractional derivatives
• fundamental solutions
• linear partial differential equations
• constructive solutions

We present and prove a new generalisation of the Malgrange-Ehrenpreis theorem to fractional partial differential equations, which can be used to construct fundamental solutions to all partial differential operators of rational order and many of arbitrary real order. We demonstrate with some examples and mention a few possible applications.

• 出版日期2017