Effect of reverse cholesterol transport on porous media type ABC fractional atherosclerosis model with memory function.

In general, high density lipoprotein is considered one of the anti-plaque acellular organisms that can reduce atherosclerotic risk by reverse cholesterol transport property. This study motivates us to propose an atherosclerosis model with Atangana-Baleanu-Caputo fractional order derivative and discuss the inflammatory and control criteria in the presence of memory function. The model includes non-linear diffusion terms to reflect the effect of porous media, as our intima is the porous media type. This research mainly focuses on mathematical analysis and simulation of the atherosclerosis inflammation process. The existence of the solution for the proposed model is discussed with the help of Picard's recursive method, and qualitative analysis is obtained. We also define the uniqueness of the proposed model. All of these analyses are presented for the corresponding kinetic system. As compared to the ordinary differential equation model, the proposed fractional-order mathematical model is more successful at determining the precise parameter values. This study clearly illustrate that atherosclerosis inflammation will be easier to identify with the use of the fractional-order mathematical model for a disease. The numerical results are demonstrated for validating the analytical results. [ABSTRACT FROM AUTHOR]