ABSTRACT
Recently, Caputo and Fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales. In this article, a finite difference scheme to solve a quasilinear fractal mobile/immobile transport model based on the new fractional derivative is introduced and analysed. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. Some a priori estimates of discrete errors with optimal order of convergence are established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.
Acknowledgments
The authors would like to thank the editor and referees for their valuable comments and suggestions which helped them to improve the results of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.