Space–time variable-order carbon nanotube model using modified Atangana–Baleanu–Caputo derivative

Abstract

Abstract This study presents a space–time variable-order fractional carbon nanotube (CNT) mathematical model. Fractional differential equations successfully describe the model and its physical and biological properties. The mathematical model simulates the mixed free convection flow of a nanofluid in porous space using single- and multi-walled CNTs. The heat transfer characteristics of the base fluid (human blood) are studied. The numerical solutions for the temperature and velocity fields were derived from the modified Atangana–Baleanu–Caputo derivative, and the model was very effective. The higher compact finite difference method is used to study the numerical technique. Stabilization is construed as a technique related to John Neumann’s stabilization analysis. Additionally, the truncation error was studied, and various graphs were used to present numerical results. The results in the tables and the numerical figures emphasize that the schemes attained from applying the submitted numerical methods are completely compatible with the exact solution.