To determine the main effects of anomalous diffusion upon the propagation of energetic particles, the fractional modified telegraph equation is solved using the Laplace–Fourier technique and given in terms of the Fox H and M-Wright functions. Examples are used to illustrate the qualitative differences between the fractional telegraph, fractional advection–diffusion and fractional diffusion equations. The profiles of the particles densities are discussed in each case for different values of fractional orders.

中文翻译：

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关于福克-普朗克方程的高能粒子传输的分数近似

为了确定异常扩散对高能粒子传播的主要影响，使用Laplace-Fourier技术求解分数修正电报方程，并根据Fox H和M- Wright函数给出。实例用于说明分数电报，分数对流扩散和分数扩散方程之间的质量差异。针对每种情况下不同分数阶值讨论了颗粒密度的分布图。