Context. Epilepsy is the most widespread disorder of the nervous system, affecting humans of all ages and races. The most common diagnostic test in epilepsy is the Electroencephalogram (EEG). Objective. In this paper, a novel automated Deep Learning (DL) approach based on integrating a pre-trained Convolutional Neural Network (CNN) structure, called AlexNet, with the Constant-Q Non-Stationary Gabor Transform (CQ-NSGT) algorithm is proposed for classifying seizure versus seizure-free EEG records. Approach. The CQ-NSGT method is introduced to transform the input 1-D EEG signal into 2-D spectrogram which is sent to the AlexNet CNN model. The AlexNet architecture is utilized to capture the discriminating features of the 2-D image corresponding to each EEG signal in order to distinguish seizure and non-seizure subjects using Multi-Layer Perceptron (MLP) algorithm. Main Results. The robustness of the introduced CQ-NSGT technique in transforming the 1-D EEG signals into 2-D spectrograms is assessed by comparing its classification results with the Continuous Wavelet Transform (CWT) method, and the results elucidate the high performance of the CQ-NSGT technique. The suggested epileptic seizure classification framework is investigated with clinical EEG data acquired from the Bonn University database, and the experimental results reveal the superior performance of the proposed framework over other state-of-the-art approaches with an accuracy of 99.56 %, sensitivity of 99.12 %, specificity of 99.67 %, and precision of 98.69 %. Significance. This elucidates the importance of the proposed automated system in helping neurologists to accurately interpret and classify epileptic EEG records without necessitating tedious visual inspection or massive data analysis for long-term EEG signals.