In this paper, we consider a class of space-time fractional inhomogeneous nonlinear diffusion equations with Riemann-Liouville fractional derivative. Symmetry group method is applied to derive explicit solutions of the governing equation from the reduced fractional ordinary differential equations. Conservation laws admitted by the space-time fractional inhomogeneous nonlinear diffusion equations are obtained with the aid of the nonlinear self-adjointness method.

中文翻译：

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时空分数阶非齐次非线性扩散方程的对称群和守恒定律

在本文中，我们考虑一类具有Riemann-Liouville 分数阶导数的时空分数阶非齐次非线性扩散方程。对称群方法用于从简化的分数阶常微分方程导出控制方程的显式解。借助非线性自邻接法，得到了时空分数阶非齐次非线性扩散方程所承认的守恒定律。