Non-Small Cell Lung Cancer (NSCLC) represents a significant health challenge globally, with high mortality rates largely attributed to late-stage diagnosis. This paper details a novel approach for denoising computed tomography (CT) scans through 2-dimensional Fractional Fourier transform (2D-FrFT), which has been reported to be effective for time-frequency signal/image processing applications. To establish a foundation for the FrFT filtering of the original and corrupt dataset, a variable fractional-order image processing technique was used. Based on the derived pre-processing of CT scans, a classification model was developed with hand-crafted features and a 2-layer neural network to classify 4834 CT scans collected from the Lung Image Database Consortium image (LIDC-IDRI) dataset into classes of normal lungs and NSCLC infected lungs. This work presents an approach to improving the performance of NSCLC detection through a lightweight neural network that attains 1.00 accuracy, 1.00 sensitivity, and 1.00 AUC. An additional real-time lung cancer dataset from PGI Rohtak, Haryana, has been considered to validate the model and prove its performance against overfitting.  The experimental analysis showed better results than the existing methods for both LIDC-IDRI and hospital datasets and could be a competent assistant to clinicians in detecting NSCLC.