  Many physical problems can be described using the integral equations known as
Volterra equations. There exists quite a number of analytical methods that can
handle these equations for linear cases. For non-linear cases, a numerical
scheme is needed to obtain an approximation. Recently a new concept of
fractional differentiation was introduced using the Mittag-Leffler function as
kernel, and the associate fractional integral was also presented. Up to this
point there is no numerical approximation of this new integral in the
literature. Therefore, to accommodate researchers working in the field of
numerical analysis, we propose in this paper a new numerical scheme for the new
fractional integral. To test the accuracy of the new numerical scheme, we first
revisit the groundwater model within a leaky aquifer by reverting the time
classical derivative with the Atangana-Baleanu fractional derivative in Caputo
sense. The new model is solved numerically by using this new scheme.
