Electron. J. Differential Equations, Vol. 2019 (2019), No. 21, pp. 1-13.

Fundamental solutions and Cauchy problems for an odd-order partial differential equation with fractional derivative

Arsen Pskhu

Abstract:
In this article, we construct a fundamental solution of a higher-order equation with time-fractional derivative, give a representation for a solution of the Cauchy problem, and prove the uniqueness theorem in the class of functions satisfying an analogue of Tychonoff's condition.

Submitted July 4, 2018. Published February 4, 2019.
Math Subject Classifications: 35R11, 35G10.
Key Words: Fractional derivative; higher order PDE; Cauchy problem.

Show me the PDF file (262 KB), TEX file for this article.

Arsen Pskhu
Institute of Applied Mathematics and Automation KBSC RAS
Nalchik, Russia
email: pskhu@list.ru

Return to the EJDE web page