Numerical solutions: solutions of ordinary and fractional order reaction diffusion equations biological models

This book develops a mathematical and computational framework for studying diabetic atherosclerosis through ordinary and fractional-order reaction-diffusion equations. It models the spatial and temporal interactions among glucose, insulin, beta cells, LDL, HDL, reactive oxygen species, macrophages, foam cells, lipoprotein(a), C-reactive protein, and cellular damage. Caputo and Caputo-Fabrizio derivatives are used to represent memory effects and anomalous diffusion in biological processes, while finite-difference simulations compare healthy, diabetic, and stress-affected conditions. The book also presents steady-state and stability analyses, existence and uniqueness results, energy estimates, and analytical and numerical solution techniques. The findings show how chronic psychosocial stress can intensify oxidative burden, disrupt metabolic regulation, and accelerate plaque formation. By connecting fractional calculus, nonlinear partial differential equations, and biomedical interpretation, the book offers a quantitative resource for researchers and graduate students in applied mathematics, mathematical biology, and computational medicine.