Numerical and Analytical Approaches to Fractional Quantum Mechanics

Our research meticulously navigates the realms of Fractional Quantum Mechanics (FQM), focusing on a critical examination of both numerical and analytical methods that harness the potential of fractional calculus to illuminate the quantum world's complexities. By embarking on this scholarly journey, we aim to decode the intricate dynamics that fractional equations reveal about quantum systems, pushing the boundaries of conventional quantum mechanics. This comparative study meticulously evaluates the efficacy and insights provided by these two distinct approaches, highlighting their contributions to a deeper understanding of quantum phenomena. As we traverse through the layers of quantum dynamics, our work seeks to contribute significantly to the theoretical framework of FQM, offering innovative perspectives and methodologies. The essence of this research lies in its potential to forge new theoretical pathways and inspire further exploration in the quantum domain, leveraging the unique capabilities of fractional calculus. By enriching the scientific community with our findings, we aspire to open new horizons in the study of quantum mechanics, marking a step forward in the ongoing quest to unravel the mysteries of the quantum universe.