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arXiv · 1405.7532

Conservation laws for time-fractional subdiffusion and diffusion-wave equations

Stanislav Yu. Lukashchuk
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Abstract

The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the Riemann-Liouville and Caputo time-fractional derivatives. It is shown that these equations are nonlinearly self-adjoint and therefore desired conservation laws can be obtained using appropriate formal Lagrangians. Fractional generalizations of the Noether operators are also proposed for the equations with the Riemann-Liouville and Caputo time-fractional derivatives of order $α\in (0,2)$. Using these operators and formal Lagrangians, new conserved vectors have been constructed for the linear and nonlinear fractional subdiffusion and diffusion-wave equations corresponding to its Lie point symmetries.

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Stanislav Yu. Lukashchuk. 2014-05-29. Conservation laws for time-fractional subdiffusion and diffusion-wave equations. https://arxiv.org/abs/1405.7532

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