Fractional Calculus

An Introduction for Physicists

The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area.

The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights.

This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject.

Contents:

• Introduction
• Functions
• The Fractional Derivative
• Friction Forces
• Fractional Calculus
• The Fractional Harmonic Oscillator
• Wave Equations and Parity
• Nonlocality and Memory Effects
• Fractional Calculus in Multidimensional Space — 2D-Image Processing
• Fractional Calculus in Multidimensional Space — 3D-Folded Potentials in Cluster Physics
• Quantum Mechanics
• The Fractional Schrödinger Equation with the Infinite Well Potential — Numerical Results using the Riesz Derivative
• Uniqueness of a Fractional Derivative — the Riesz and Regularized Liouville Derivative as Examples
• 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
• 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

Readership: Students and researchers in physics.
Key Features:

• This was the first book on the market covering the full area of a physical application of fractional calculus
• The book provides a skillful insight into a vividly growing research area and guides the reader from his first steps on an introductory level up to the current state of the art of a physical interpretation and application in different fields
• This book enables the reader to participate and contribute to the development of this exciting research area by applying these methods in his own research area too