We use a concept of weak asymptotic solution for homogeneous as well asnon-homogeneous fractional advection dispersion type equations. Using Legendrescaling functions as basis, a numerical method based on Galerkin approximationis proposed. This leads to a system of fractional ordinary differentialequations whose solutions in turn give approximate solution for theadvection-dispersion equations of fractional order. Under certain assumptionson the approximate solutions, it is shown that this sequence of approximatesolutions forms a weak asymptotic solution. Numerical examples are given toshow the effectiveness of the proposed method.
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