By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, numerical solutions of time-fractional diffusion equation are discussed. Again, through another similarity transformation, nonlinear model of space-fractional diffusion/Harry Dym equation is turned into corresponding ordinary differential equations, whose two similarity solutions are also worked out.

中文翻译：

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非线性扩散/哈里动力分数阶方程的相似解

通过标量相似变换，将时间分数阶扩散/ Harry Dym方程的非线性模型转换为相应的常分数阶微分方程，从中给出了时间分数分数Harry Dym方程的行波相似解。此外，讨论了时间分数阶扩散方程的数值解。再次，通过另一次相似性变换，将空间分数扩散/ Harry Dym方程的非线性模型转换为相应的常微分方程，并求解了它们的两个相似性解。