Exploring the Applications of Burger's Equation in Modeling Skin Cancer Progression and Asset Price Dynamics

This study explores the application of Burger's equation, a nonlinear partial differential equation, in modeling phenomena in both biomedical and financial contexts. Specifically, it investigates the progression of skin cancer and the dynamics of asset prices. The research demonstrates the versatility of Burger's equation in capturing complex behaviors in disparate fields, offering insights into tumor growth and market volatility. The findings suggest that mathematical models like Burger's equation can provide unified approaches to solving problems in diverse areas, enhancing predictive accuracy and decision-making. This study explores the innovative application of Burger's equation in modeling two distinct complex systems: skin cancer progression and asset price dynamics. Burger's equation, a fundamental nonlinear partial differential equation known for its ability to capture the interplay between advection and diffusion, is adapted and extended to address the unique challenges presented by these fields. In the context of skin cancer, the equation is modified to incorporate biological processes such as cell proliferation, apoptosis, and nutrient diffusion, providing a detailed and accurate simulation of tumor growth dynamics. In the financial domain, the equation is tailored to include nonlinear market sentiment effects and stochastic elements to reflect realistic asset price movements and volatility. Numerical simulations and sensitivity analyses validate the models against empirical data, demonstrating their robustness and predictive power. The results highlight the equation's versatility, offering new insights and practical applications in oncology and financial markets. This interdisciplinary approach underscores the potential of mathematical modeling to advance research and improve decision-making across diverse scientific and economic domains.