NUMERICAL SIMULATION TO INVESTIGATE THE BEHAVIOR OF THE BONE REMODELING PROCESS IN HEALTHY AND TUMOROUS BONE USING FRACTIONAL DERIVATIVES WITH TIME-DELAY

Abstract

Bone remodeling is the intricate process responsible for the repairing of old and damaged bone within the human body. Nonetheless, this cycle can be disrupted by various factors, leading to bone diseases such as osteoporosis. In this research, we investigate bone remodeling in both healthy and tumorous bone tissues, using the fractional derivatives technique and time delay method in our model. We also provide a numerical solution of the influence of various parameters on this cycle. The results present that both the order of the fractional derivative and the time delay significantly impact the model's behavior. Specifically, higher orders of the fractional derivative and the greater amount of time delays contribute to a more rapid progression of the modeled dynamics compared to the original model.