Analysis and numerical simulation of fractional-order blood alcohol model with singular and non-singular kernels

Abstract

In this manuscript, we examine the blood alcohol model to investigate the dynamics of alcohol concentration in the human body. The classical model of blood alcohol concentration is converted into the fractional model by using Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo derivatives. The existence and uniqueness theory for the model’s solution is constructed using the Banach fixed point theory. Also, the stability of the solution is established by Ulam-Hyers conditions. For the numerical simulation of the considered model, the Adams-Bashforth method with a two-step Lagrange polynomial is used and the numerical solution of the model with three different derivatives is presented in the tabular and graphical form. The comparison between the exact solution and observed solution is made by root mean square technique which is found to be in good agreement. Finally, the results from the three fractional derivatives are also compared with the exact data, which revealed that the CF fractional derivative performs better than the other two fractional derivatives.

Keywords

• blood alcohol model
• caputo fractional derivative
• caputo-fabrizio fractional derivative
• atangana-baleanu-caputo derivatives
• fixed point theorem
• ulam-hyers stability
• adams-bashforth method
• 26a33
• 65l99
• 34a08