The COVID-19 pandemic, which originated in 2019, has caused a significant global number of fatalities. The economic and healthcare impacts of COVID-19 infection in survivors have become evident during this period. An important first step towards the effective management of COVID-19 is an effective screening of patients, which includes radiology examinations using chest radiography as one of the primary screening modalities. Early research has shown that patients with pneumonia and COVID-19 infection show different anomalies in chest radiography images. Classifying images of COVID-19 and pneumonia diseases has proven to be a challenging task for computers. Several classification systems were developed using different databases in order to determine the category to which the detected image belongs. The accuracy percentage was assessed using these systems. However, there are instances where the imaging techniques may produce distorted images, low contrast images, or fail to accurately depict the edges of the internal organs. These challenges can have an impact on the accuracy of a classification model's design. In this study, a new robust model called FPD-VGG-16 is introduced. This model combines the Visual Geometry Group (VGG-16) deep learning technique with the Fractional Partial Differential (FrPDA) mathematical method. The idea of using FrPDA is to improve edges, increase the visibility of texture details, and retain smooth areas in comparison to using only deep algorithms. The proposed model demonstrates accurate pneumonia detection and COVID-19 classification from chest X-ray images; the model recorded an impressive accuracy of 98.1%, along with equally remarkable precision and recall values 0.982 and 0.980 respectively, as well as and f1-score score of 0.981. While 96.2% as an accuracy measure is achieved in this study without using the FrPDA algorithm.