Nonlocal and fractional operators / / Luisa Beghin, Francesco Mainardi, Roberto Garrappa, editors

• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (314 pages)
• Disciplina: 515
• Soggetto topico: Fractional calculus; Operator theory; Càlcul fraccional; Teoria d'operadors
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): BeghinLuisa; MainardiFrancesco; GarrappaRoberto
• Nota di contenuto: Intro -- Preface -- Presentation of the Workshop "Nonlocal and Fractional Operators" Dedicated to Prof. Renato Spigler (Rome, April 12-13, 2019) -- Contents -- On the Transient Behaviour of Fractional M/M/infty Queues -- 1 Introduction -- 2 The M/M/infty Queue -- 3 The Fractional M/M/infty Queue -- 3.1 Definition of the Queue and the Main Quantities -- 3.2 Fractional Equations for the State Probabilities and the Generating Function -- 3.3 Laplace Transforms of pnν(t) and Gν(z,t) -- 3.4 Mean and Variance of the Process -- 4 Interpretation of Nν(t) as a Queue -- 4.1 Inter-arrival, Inter-event and Inter-exit Times -- 4.2 Virtual Waiting Times for the Fractional M/M/infty -- 4.3 Virtual Waiting Times for the Fractional M/M/1 Queue with Responsive Server -- References -- Sinc Methods for Lévy-Schrödinger Equations -- 1 Introduction -- 2 Approximation Method -- 2.1 Sinc Methods -- 2.2 Discretization Formula -- 2.3 Sinc Collocation of Fractional Sturm-Liouville Problems -- 3 Numerical Results -- 3.1 Harmonic Oscillator -- 3.2 Quarkonium Models -- 3.3 Finite Quantum Well -- 4 Conclusions -- 5 Appendix -- References -- Stochastic Properties of Colliding Hard Spheres in a Non-equilibrium Thermal Bath -- 1 Introduction -- 2 Collision Theory and Stochastic Differential Equation -- 3 Molecular Dynamics Simulations -- 4 Conclusions -- References -- Electromagnetic Waves in Non-local Dielectric Media: Derivation of a Fractional Differential Equation Describing the Wave Dynamics -- 1 Introduction -- 2 The Model "Classical Approach" -- 3 Fractional Operator Approach -- 4 The 1D Fractional Wave Equation -- 5 Conclusions -- Appendix 1. Derivation of the Integral Wave Equation for Wave Propagation in Non-Homogeneous Plasma -- References -- Some New Exact Results for Non-linear Space-Fractional Diffusivity Equations -- 1 Introduction. ; 2 The Real Gas Diffusivity Equation: Classical Models and Fractional Generalization -- 3 Diffusivity Models with Permeability Variations Induced by Variations of Pressure -- 3.1 Exact Analytical Results -- 4 Conclusions -- 5 Appendix A: Some Details on Fractional Caputo Derivatives -- 6 Appendix B: The Invariant Subspace Method -- 7 Appendix C: A Mathematical Analysis of the More General Case -- References -- A Note on Hermite-Bernoulli Polynomials -- 1 Introduction -- 2 Generalized Hermite Polynomials and Bernoulli Polynomials -- 3 Further Generalizations of Hermite-Bernoulli Polynomials -- 4 Application to Fractional-Order Operators and Concluding Remarks -- References -- A Fractional Hawkes Process -- 1 Introduction -- 2 Mittag-Leffler Distributed Positive Random Variables -- 3 The Fractional Hawkes Processes -- 3.1 Spectral Properties -- 3.2 Intensity Expectation -- 4 Simulation -- 5 Outlook -- References -- Fractional Diffusive Waves in the Cauchy and Signalling Problems -- 1 Introduction -- 2 The Wright Function and the Mainardi Auxiliary Functions -- 3 Cauchy and Signaling Problems: Green Functions for Fractional Diffusive Waves -- 4 Cauchy and Signaling Problems: Box Evolution for Fractional Diffusive Waves -- 4.1 Solutions for the Cauchy Problem -- 4.2 Solutions for the Signaling Problem -- 5 Interpretation of the Green Functions as Diffusive Waves -- 5.1 Cauchy Problem -- 5.2 Signaling Problem -- 6 Multi-dimensional Fractional Diffusion-Wave Equation -- 7 Conclusions -- 8 Appendix A: Fractional Calculus: An Introduction -- References -- Some Extension Results for Nonlocal Operators and Applications -- 1 Some Nonlocal Operators -- 2 Extension Approach to Nonlocal Operators -- 2.1 The Marchaud Case -- 2.2 Carnot Setting -- 2.3 The Extension Approach in Carnot Groups -- 3 Applications -- 3.1 Weyl-Marchaud Derivative: The Harnack Inequality. ; 3.2 Fractional Operators of Sublaplacians in Carnot Groups: The Harnack Inequality -- 3.3 Carnot Groups: A Perimeter Notion -- 4 Extension Approach: The Periodic Function Case via Fourier Series Tool -- 4.1 The Case s=12 -- 4.2 General Case with Bessel Functions: A Short Remark -- References -- The Pearcey Equation: From the Salpeter Relativistic Equation to Quasiparticles -- 1 The Salpeter Equation: An Historical Review from Classical to Quantum Mechanics -- 2 The Pearcey Equation -- 3 Evolution of the Lorentzian Wave Packet -- 4 Quantum Caustics and Light-Cone Structure: The Onset of Granularity in the Nature of the Light-Cone Structure -- References -- Recent Developments on Fractional Point Processes -- 1 Introduction -- 2 Fractional Poisson Process -- 3 Interlinking the Fractional Operators, the Lévy Process and the Poisson Process -- 3.1 Lévy Subordinator -- 3.2 Fractional Poisson Process and Lévy Subordinator -- 4 More Results on Fractional Point Processes -- 5 Plots and Simulations of Fractional Poisson Process -- References -- Some Results on Generalized Accelerated Motions Driven by the Telegraph Process -- 1 Introduction -- 2 Explicit Conditional Distribution for Small n -- 3 Unconditional Mean and Variance -- References -- The PDD Method for Solving Linear, Nonlinear, and Fractional PDEs Problems -- 1 Introduction -- 2 Linear Parabolic Problems -- 2.1 Introduction -- 2.2 Mathematical Preliminaries -- 2.3 The Numerical Method -- 2.4 Summary -- 3 Semilinear Parabolic Problems -- 3.1 Introduction -- 3.2 A Generalized Probabilistic Representation for Semilinear Parabolic Problems -- 3.3 Summary -- 4 The Vlasov-Poisson System for Plasma Physics -- 4.1 Introduction -- 4.2 Probabilistic Representation for the Vlasov-Poisson System -- 4.3 Evaluating Numerically the Probabilistic Representation of Vlasov-Poisson -- 4.4 Summary. ; 5 Fractional Partial Differential Boundary-Value Problems -- 6 Conclusions -- References -- Fractional Diffusion and Medium Heterogeneity: The Case of the Continuous Time Random Walk -- 1 Introduction and Motivation -- 2 Markovian Random Walk in a Heterogeneous Medium -- 3 The Emerging of Fractional Diffusion -- 4 Numerical Simulations and Discussion -- 5 Conclusions -- References -- On Time Fractional Derivatives in Fractional Sobolev Spaces and Applications to Fractional Ordinary Differential Equations -- 1 Introduction and Main Results -- 1.1 Generalized Time-Fractional Derivative -- 1.2 Caputo Derivative of the Order 1 < -- α< -- 2 in Sobolev Spaces -- 2 Proof of Theorem 1 -- 3 Proof of Theorem 3 -- 4 Application to Generalized Caputo Fractional Ordinary Differential Equations -- 5 Applications to Caputo Fractional Ordinary Differential Equations of Order 1< -- α< -- 2 -- 6 Concluding Remarks on Future Topics -- References.
• Titolo autorizzato: Nonlocal and fractional operators
• ISBN: 3-030-69236-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466404903316
• Lo trovi qui: Univ. di Salerno
• Serie: SEMA SIMAI Springer series ; ; Volume 26.