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Open AccessArticle

Exact Solutions and Conservation Laws of Time-Fractional Levi Equation

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
Symmetry 2020, 12(7), 1074; https://doi.org/10.3390/sym12071074
Received: 5 May 2020 / Revised: 21 June 2020 / Accepted: 21 June 2020 / Published: 30 June 2020
Exact solutions were derived for a time-fractional Levi equation with Riemann–Liouville fractional derivative. The methods involve, first, the reduction of the time-fractional Levi equation to fractional ordinary differential equations with Erdélyi-Kober fractional differential operator with respect to point symmetry groups, and second, use of the invariant subspace to reduce the time-fractional Levi equation into a system of fractional ordinary differential equations, which were solved by the symmetry group method. The obtained explicit solutions have interesting analytic behaviors connected with blow-up and dispersion. The conservation laws generated by the point symmetries of the time-fractional Levi equation are shown via nonlinear self-adjointness method.
Keywords: time-fractional Levi equation; conservation laws; invariant subspace; exact solutions time-fractional Levi equation; conservation laws; invariant subspace; exact solutions
MDPI and ACS Style

Feng, W. Exact Solutions and Conservation Laws of Time-Fractional Levi Equation. Symmetry 2020, 12, 1074.

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