Fractional calculus is undergoing rapid and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics.
This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in the subjects of classical mechanics, friction, damping, oscillations, group theory, quantum mechanics, nuclear physics, and hadron spectroscopy up to quantum field theory.
Contents:
Functions
The Fractional Derivative
Friction Forces
Fractional Calculus
The Fractional Harmonic Oscillator
Wave Equations and Parity
Nonlocality and Memory Effects
Quantum Mechanics
Fractional Spin: A Property of Particles Described with the Fractional Schrödinger Equation
Factorization
Symmetries
The Fractional Symmetric Rigid Rotor
q-Deformed Lie Algebras and Fractional Calculus
Fractional Spectroscopy of Hadrons
Higher Dimensional Fractional Rotation Groups
Fractors: Fractional Tensor Calculus
Fractional Fields
Gauge Invariance in Fractional Field Theories
Outlook