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首页> 外文期刊>International journal of non-linear mechanics >Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus
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Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus

机译：在分数演算范围内模拟杂质和熔融氧浓度的进展

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摘要

The model describing the mitigation of contamination through ventilation inside a moving waterway polluted via dispersed bases together with connected reduction of liquefied oxygen was investigated within the scope of fractional derivatives. The steady-state cases were investigated using some Caputo derivatives properties. The steady-state solutions in presence and absence of the dispersion were derived in terms of the Mittag-Leffler function. In the case of non-steady state, we derived the solution of the first equation in terms of the α-stable error function via the Laplace transform method. To solve the second equation, we constructed the fractional Green function via the Laplace, Fourier and Mellin transforms. The fractional Green function was expressed by mean of the H-function. Particularly, we presented the selected numerical results a function of distance and α.
机译：在分数导数的范围内，研究了描述通过移动的水道通风进行的污染减轻模型，该运动的水道经分散的碱污染并与液化氧联系起来还原。使用Caputo衍生物的某些特性研究了稳态情况。根据Mittag-Leffler函数推导存在和不存在分散液的稳态溶液。在非稳态情况下，我们通过Laplace变换方法根据α稳定误差函数推导了第一方程的解。为了解决第二个方程，我们通过Laplace，Fourier和Mellin变换构造了分数格林函数。分数格林函数通过H函数表示。特别是，我们将所选数值结果呈现为距离和α的函数。

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