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

Electronic Journal of Qualitative Theory of Differential Equations

Dumitru Baleanu¹  Arran Fernandez² 

[1] Cankaya University, Department of Mathematics and Computer Sciences, Ankara, Turkey & Institute of Space Sciences, Magurele-Bucharest, Romania;Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK;

关键词: fractional derivatives;    fundamental solutions;    linear partial differential equations;    constructive solutions;   

DOI  :  10.14232/ejqtde.2017.1.15

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown