Alzheimer's disease (AD), a prevalent neurological condition, poses a multifaceted challenge affecting millions worldwide. It demands diverse solutions, both pharmaceutical and non-pharmaceutical, to ameliorate symptoms and enhance patients' quality of life across various stages. Tailored intervention strategies are essential for addressing AD's progression, emphasizing the significance of early detection and stage classification. This study underscores the pivotal role of medical imaging, specifically MRI, in AD diagnosis and monitoring. MRI interpretation is often time-consuming and relies on clinical intuition, necessitating more efficient and accurate approaches. In response, a custom convolutional neural network (CNN) model named ALSA-3 and deep learning (DL) techniques are explored for MRI-based alzheimer's disease classification. Various image processing techniques, such as MSE, RMSE, PSNR, and SSIM, enhance image quality. An ablation study systematically adjusts hyperparameters and layer structures. Results showcase the superiority of the proposed ALSA-3 model over traditional methods, achieving an exceptional 99.50% accuracy, with precision, F1-score, and recall values of 100%, 99%, and 99%. Model robustness is evaluated with different k values, reinforcing its efficacy in alzheimer's disease classification. Moreover, the elucidation of the ALSA-3 model incorporates grad-cam and grad-cam++ explainable artificial intelligence (XAI) techniques, to furnish comprehensive explanations elucidating the clarify the reasoning behind model decisions. This study not only advances state-of-the-art in alzheimer's disease classification but also holds the potential to significantly benefit patients, caregivers, and the medical community. The improved accuracy and efficiency of our model promise more accurate and timely diagnosis, thereby enhancing the lives of those affected by alzheimer's disease.