More generalized groundwater model with space-time Caputo Fabrizio fractional differentiation

2016/10/24 by J-D Djida, Djida, J-D, Abdon Atangana +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1610.07345

openalex publication_date 2016/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove existence and uniqueness of the flow of water within a confined aquifer with fractional diffusion in space and fractional time derivative in the sense of Caputo-Fabrizio. Our main method is the fixed-point theorem. We propose the numerical approximation of the model. The Crank-Nicolson numerical scheme was used to solve the modified model. In order to check the effectiveness of the model, stability analysis of the numerical scheme for the new model are presented.

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