This paper proposes an idea to predict the probability density function (PDF) of the aircraft waiting time before landing using a physics-based methodology. The data is derived from the Sherlock Data Warehouse near Atlanta International Airport (KATL) from August 1st to August 31st. Aircraft waiting time is defined as the time used for a single aircraft flying from 100 nautical mile to 40 nautical mile away from KATL. A density-based spatial clustering of applications with noise (DBSCAN) and kernel density estimation is used for denoising and creating smooth PDF respectively. After that, a PDE-FIND algorithm is applied for finding the governing equations of the change of PDF over time. For validation and prediction, the PDE problem is solved by a physics informed neural network (PINN) based on known data and governing equations learned from the previous step. Result shows that this method has high accuracy in predicting PDF of the aircraft waiting time especially the mean behavior and can be utilized to assist Air Traffic Management (ATM) to improve the airport efficiency.