Table of Contents

Introduction; Functions; The Fractional Derivative; Friction Forces; Fractional Calculus; The Fractional Harmonic Oscillator; Wave Equations and Parity; Nonlocality and Memory Effects; The Generalized Fractional Derivative; Fractional Calculus in Multidimensional Space - 3D-Folded Potentials; Quantum Mechanics; The Fractional Schrodinger Equation with the Infinite Well Potential; Uniqueness of a Fractional Derivative; Fractional Spin - A Property of Particles Described with the Fractional Schrodinger Equation; Factorization; Symmetries; The Fractional Symmetric Rigid Rotor; Q-Deformed Lie Algebras and Fractional Calculus; Infrared Spectroscopy of Diatomic Molecules; Fractional Spectroscopy of Hadrons; Magic Numbers in Atomic Nuclei; Magic Numbers in Metal Clusters; Fractors - Fractional Tensor Calculus; Fractional Fields; Gauge Invariance in Fractional Field Theories; On the Origin of Space; Outlook.