Financial differential equations is a field within quantitative finance and applied mathematics that utilizes differential equations to model and analyze the dynamic behavior of financial markets and instruments. This research area investigates the continuous-time evolution of financial variables, employing ordinary, partial, or stochastic differential equations to capture phenomena such as asset price movements, interest rate dynamics, and the valuation of derivative contracts. Its significance lies in providing the rigorous mathematical frameworks essential for pricing, hedging, risk management, and quantitative analysis in modern financial engineering.