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

TL;DR

This paper introduces a generalized groundwater flow model using space-time Caputo-Fabrizio fractional derivatives, proving its mathematical well-posedness and implementing a numerical scheme for simulation.

Contribution

It presents a novel fractional diffusion model for groundwater flow with proven existence and uniqueness, and develops a stable numerical approximation scheme.

Findings

The model's well-posedness is established.

The Crank-Nicolson scheme effectively approximates the model.

Stability analysis confirms the numerical method's reliability.

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.