Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus

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.