Abstract
In this article, an anomalous diffusion model via a new Liouville-Caputo general fractional operator with the Mittag-Leffler function of Wiman type is investigated for the first time. The convergence of the series solution for the problem is discussed with the aid of the Laplace transform. The anomalous diffusion processes are compared to the characteristics of the conventional diffusion graphically. The results show that the new Liouville-Caputo general fractional operator is effective in characterizing and solving the problems of the anomalous diffusion.