Direct and Inverse Source Problem for a Space Fractional Advection Dispersion Equation

In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the fundamental solution to the direct problem and we show that the relation between source and the final observation is linear. Moreover, we study the well-posedness of both problems: existence, uniqueness and stability. Finally, we illustrate the results with a numerical example.