Nikolai Laskin's paper introduces fractional quantum mechanics and fractional statistical mechanics, developed through a new path integral approach based on Lévy flights. The paper generalizes the traditional Feynman and Wiener path integrals to accommodate Lévy processes, which are more suitable for modeling anomalous diffusion, turbulence, chaotic dynamics, and other complex phenomena. The fractional quantum mechanics (fQM) and fractional statistical mechanics (fSM) are defined using path integrals that incorporate the Lévy distribution, which is a generalization of the Gaussian distribution. The author provides detailed mathematical formulations for the fractional free particle propagator, the fractional Schrödinger equation, and the fractional density matrix, demonstrating how these equations reduce to the classical counterparts in the limit of standard Brownian motion. The paper concludes by suggesting that further research should focus on applying these new theories to specific physical systems to understand their quantum dynamics and statistical mechanics.Nikolai Laskin's paper introduces fractional quantum mechanics and fractional statistical mechanics, developed through a new path integral approach based on Lévy flights. The paper generalizes the traditional Feynman and Wiener path integrals to accommodate Lévy processes, which are more suitable for modeling anomalous diffusion, turbulence, chaotic dynamics, and other complex phenomena. The fractional quantum mechanics (fQM) and fractional statistical mechanics (fSM) are defined using path integrals that incorporate the Lévy distribution, which is a generalization of the Gaussian distribution. The author provides detailed mathematical formulations for the fractional free particle propagator, the fractional Schrödinger equation, and the fractional density matrix, demonstrating how these equations reduce to the classical counterparts in the limit of standard Brownian motion. The paper concludes by suggesting that further research should focus on applying these new theories to specific physical systems to understand their quantum dynamics and statistical mechanics.