Facial expression recognition is pivotal in diverse domains such as human-computer interaction, affective computing, and psychological research. This study introduces an innovative methodology to enhance the accuracy of facial expression recognition by integrating optical flow modeling, deep feature extraction, and advanced classification algorithms. Utilizing the Non-Linear Fractional Order Variational (NFOV) model, we generate color-map images of optical flow from video sequences that portray various facial expressions. Our approach leverages optical flow to capture subtle variations in facial expressions, while exploiting the feature extraction process of SqueezeNet and the computational efficiency of Stochastic Gradient Descent (SGD). Specifically, we fine-tuned the SqueezeNet deep learning architecture, renowned for its efficiency in feature extraction, to extract salient features from these color-map images. SGD is applied for the classification task. Experimental evaluations on the CK + dataset demonstrate the efficacy of our method which achieves a classification accuracy of 79.3% and an area under the curve (AUC) of 95.7%.