A nonlocal generalization of the Exner law.

Abstract Here we consider a new, more general mathematical formulation of the nonlocal Exner law, widely used in morphodynamics and sediment transport models. In some recent literature the role of nonlocal effects in the sediment flux was analyzed, by using a fractional calculus approach, based on the application of Caputo fractional derivatives. In this paper we apply fractional derivatives of a function with respect to another function in order to have a more general and realistic picture of nonlocal effects in sediment transport models. We then discuss the meaning of this approach, considering a logarithmic profile emerging from the generalized formulation of the nonlocal steady Exner law. We finally suggest that this can be the way to overcome the theoretical shortcomings of the fractional Exner equation based on the application of classical Caputo derivatives.