In the current research study, a new method is presented to diagnose Anterior Cruciate Ligament (ACL) tears by introducing an optimized version of the InceptionV4 model. Our proposed methodology utilizes a custom-made variant of the Snow Leopard Optimization Algorithm, known as the Fractional-order Snow Leopard Optimization Algorithm (FO-LOA), to extract essential features from knee magnetic resonance imaging (MRI) images. This results in a substantial improvement in the accuracy of ACL tear detection. By effectively extracting critical features from knee MRI images, our proposed methodology significantly enhances diagnostic accuracy, potentially reducing false negatives and false positives. The enhanced model based on FO-LOA underwent thorough testing using the MRNet dataset, demonstrating exceptional performance metrics including an accuracy rate of 98.00%, sensitivity of 98.00%, precision of 97.00%, specificity of 98.00%, F1-score of 98.00%, and Matthews Correlation Coefficient (MCC) of 88.00%. These findings surpass current methodologies like Convolutional Neural Network (CNN), Inception-v3, Deep Belief Networks and Improved Honey Badger Algorithm (DBN/IHBA), integration of the CNN with an Amended Cooking Training-based Optimizer version (CNN/ACTO), Self-Supervised Representation Learning (SSRL), signifying a significant breakthrough in ACL injury diagnosis. Using FO-SLO to optimize the InceptionV4 framework shows promise in improving the accuracy of ACL tear identification, enabling prompt and efficient treatment interventions.