Alzheimer's disease is a neurodegenerative condition primarily attributed to environmental factors, abnormal protein deposits, immune system dysregulation, and the consequential death of nerve cells in the brain. On the other hand, Parkinson's disease manifests as a neurological disorder featuring primary motor, secondary motor, and non-motor symptoms, accompanied by the rapid demise of cells in the brain's dopamine-producing region. Utilizing brain images for accurate diagnosis and treatment is integral to addressing both conditions. This study harnessed the power of artificial intelligence for classification processes, employing state-of-the-art transformer models such as Swin Transformer, Vision Transformer (ViT), and Bidirectional Encoder representation from Image Transformers (BEiT). The investigation utilized an open-source dataset comprising 450 images, evenly distributed among healthy, Alzheimer's, and Parkinson's classes. The dataset was meticulously divided, with 80% allocated to the training set (390 images) and 20% to the validation set (90 images). Impressively, the classification accuracy surpassed 80%, showcasing the efficacy of transformer-based models in disease detection. Looking ahead, this study recommends delving into hybrid and ensemble models and leveraging the strengths of multiple transformer-based deep learning architectures. Beyond contributing crucial insights at the intersection of artificial intelligence and neurology, this research emphasizes the transformative potential of advanced models for enhancing diagnostic precision and treatment strategies in Alzheimer's and Parkinson's diseases. It signifies a significant step towards integrating cutting-edge technology into mainstream medical practices for improved patient outcomes.