Solution of a fractional transport equation by using the generalized quadratic form

In this manuscript the one dimensional fractional transport equation in which the prescribed source and angular flux are spatially quadratic is investigated within the generalized quadratic form method. It is reported that the angular flux satisfies Fick’s law and the corresponding scalar flux satisfies the fractional generalization of the classic diffusion equation.

Research highlights
► The generalized the quadratic form method was developed.
► The one-dimensional fractional transport equation was investigated.
► It was proved that the angular flux satisfies Fick’s law.
► It was proved that the scalar flux satisfies the fractional generalization of the classic diffusion equation.