Fractional Calculus (ePub)

-->The book presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and contribute in the development of this exciting research area.This book is devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights.This new, extended edition includes additional chapters about numerical solution of the fractional Schrödinger equation, self-similarity and the geometric interpretation of non-isotropic fractional differential operators. Motivated by the positive response, new exercises with elaborated solutions are added, which significantly support a deeper understanding of the general aspects of the theory.Besides students as well as researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject. -->Contents:IntroductionFunctionsThe Fractional DerivativeFriction ForcesFractional CalculusThe Fractional Harmonic OscillatorWave Equations and ParityNonlocality and Memory EffectsFractional Calculus in Multidimensional Space — 2D-Image ProcessingFractional Calculus in Multidimensional Space — 3D-Folded Potentials in Cluster Physics — A Comparison of Yukawa and Coulomb Potentials with Riesz Fractional IntegralsQuantum MechanicsThe Fractional Schrödinger Equation with Infinite Well Potential — Numerical Results Using the Riesz DerivativeUniqueness of a Fractional Derivative — The Riesz and Regularized Liouville Derivative as ExamplesFractional Spin — A Property of Particles Described with the Fractional Schrödinger EquationFactorizationSymmetriesThe Fractional Symmetric Rigid Rotorq-Deformed Lie Algebras and Fractional Calculus Infrared Spectroscopy of Diatomic MoleculesFractional Spectroscopy of HadronsMagic Numbers in Atomic NucleiMagic Numbers in Metal ClustersTowards a Geometric Interpretation of Generalized Fractional IntegralsFractors — Fractional Tensor CalculusFractional FieldsGauge Invariance in Fractional Field TheoriesNumerical Solution of the Fractional Schrödinger Equation via Diagonalization — A Plea for the Harmonic Oscillator Basis. Part I: The One Dimensional CaseOn the Origin of SpaceOutlook --> -->Readership: Students, researchers as well as lecturers of various physics courses. -->Mathematical Physics;Fractional Calculus;Long-Memory Kernels;Non-Local Field Theories;Fractional Quantum Mechanics0Key Features:This is the only book in the market covering the full area of a physical application of fractional calculusThis book provides a skillful insight into a vividly growing research area and guides the reader from the introductory level up to the current state-of-the-art of a physical interpretation and application in different fieldsThis book enables the reader to participate and contribute in the development of this exciting research area and to apply these methods in his own research area too