Symmetry structure of multi-dimensional time-fractional partial differential equations

Zhi-Yong Zhang; Jia Zheng

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arXiv · 1912.08602

Symmetry structure of multi-dimensional time-fractional partial differential equations

Zhi-Yong Zhang·Jia Zheng

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Abstract

In this paper, we concentrate on the Lie symmetry structure of a system of multi-dimensional time-fractional partial differential equations (PDEs). Specifically, we first give an explicit prolongation formula of the Lie infinitesimal generator involving time-fractional partial derivative in multi-dimensional case, and then show that the admitted infinitesimal generator has an elegant structure. Furthermore, we present two simple conditions to determine the infinitesimal generator where one is a system of linear time-fractional PDEs, the other is a system of integer-order PDEs and plays the dominant role in the whole procedure. We study three time-fractional PDEs to illustrate the efficiency of the results.

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Zhi-Yong Zhang, Jia Zheng. 2019-12-14. Symmetry structure of multi-dimensional time-fractional partial differential equations. https://arxiv.org/abs/1912.08602

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