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

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.

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

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