Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation

Advances in Difference Equations

Rubayyi T Alqahtani¹  Abdon Atangana² 

[1] Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia;Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, Bloemfontein, South Africa

关键词: Caputo-Fabrizio derivative;    numerical approximation;    advection diffusion equation;    stability analysis;   

DOI  :  10.1186/s13662-016-0871-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Recently, Caputo and Fabrizio proposed a new derivative with fractional order without singular kernel. The derivative has several interesting properties that are useful for modeling in many branches of sciences. For instance, the derivative is able to describe substance heterogeneities and configurations with different scales. In order to accommodate researchers dealing with numerical analysis, we propose a numerical approximation in time and space. We modified the advection dispersion equation by replacing the time derivative with the new fractional derivative. We solve numerically the modified equation using the proposed numerical approximation. The stability and convergence analysis of the numerical scheme were presented together with some simulations.

【 授权许可】

CC BY