@article{Arshad2023, 
author = {Sadia Arshad and Iram Saleem and Ali Akgül and Jianfei Huang and Yifa Tang and Sayed M Eldin},
title = {A novel numerical method for solving the Caputo-Fabrizio fractional differential equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {9535-9556},
keywords = {fractional differential equation, non-singular operator, numerical approximation, stability analysis, convergence analysis},
url = {https://www.sciopen.com/article/10.3934/math.2023481},
doi = {10.3934/math.2023481},
abstract = {In this paper, a unique and novel numerical approach—the fractional-order Caputo-Fabrizio derivative in the Caputo sense—is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's    1      /    3 rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings.}
}