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Advanced Mathematical Methods : Theory and Applications / / Andrea Giusti, Francesco Mainardi
| Advanced Mathematical Methods : Theory and Applications / / Andrea Giusti, Francesco Mainardi |
| Autore | Giusti Andrea |
| Pubbl/distr/stampa | [Place of publication not identified] : , : MDPI - Multidisciplinary Digital Publishing Institute, , 2020 |
| Descrizione fisica | 1 online resource (198 pages) |
| Disciplina | 511.3 |
| Soggetto topico | Proof theory |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Altri titoli varianti | Advanced Mathematical Methods |
| Record Nr. | UNINA-9910688581903321 |
Giusti Andrea
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| [Place of publication not identified] : , : MDPI - Multidisciplinary Digital Publishing Institute, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Advanced Mathematical Methods : Theory and Applications / / edited by Andrea Giusti, Francesco Mainardi
| Advanced Mathematical Methods : Theory and Applications / / edited by Andrea Giusti, Francesco Mainardi |
| Pubbl/distr/stampa | [Place of publication not identified] : , : MDPI AG, , 2020 |
| Descrizione fisica | 1 online resource (198 pages) |
| Disciplina | 511.8 |
| Soggetto topico | Mathematical models |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Special Issue Editors -- Special Issue Information -- Keywords -- Published Papers. |
| Altri titoli varianti | Advanced Mathematical Methods |
| Record Nr. | UNINA-9910598019903321 |
| [Place of publication not identified] : , : MDPI AG, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Fractional Calculus : Theory and Applications / / Francesco Mainardi, editor
| Fractional Calculus : Theory and Applications / / Francesco Mainardi, editor |
| Pubbl/distr/stampa | Basel, Switzerland : , : MDPI, , 2018 |
| Descrizione fisica | 1 online resource (208 pages) |
| Disciplina | 515.83 |
| Soggetto topico | Fractional calculus |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Altri titoli varianti | Fractional Calculus |
| Record Nr. | UNINA-9910674383403321 |
| Basel, Switzerland : , : MDPI, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Fractional calculus : theory and applications / / edited by Francesco Mainardi
| Fractional calculus : theory and applications / / edited by Francesco Mainardi |
| Pubbl/distr/stampa | Basel, Switzerland : , : MDPI, , [2018] |
| Descrizione fisica | 1 online resource (208 pages) : illustrations |
| Disciplina | 515.83 |
| Soggetto topico | Fractional calculus |
| ISBN | 3-03897-207-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Altri titoli varianti | Fractional Calculus |
| Record Nr. | UNINA-9910765799003321 |
| Basel, Switzerland : , : MDPI, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mittag-Leffler Functions, Related Topics and Applications [[electronic resource] /] / by Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin
| Mittag-Leffler Functions, Related Topics and Applications [[electronic resource] /] / by Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin |
| Autore | Gorenflo Rudolf |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (454 p.) |
| Disciplina | 515.83 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Special functions
Mathematical physics Mathematical models Integral equations Probabilities Special Functions Mathematical Applications in the Physical Sciences Mathematical Modeling and Industrial Mathematics Integral Equations Probability Theory and Stochastic Processes |
| ISBN | 3-662-43930-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Introduction -- 1.History of Mittag-Leffler functions -- 2.Classical Mittag-Leffler function -- 3.Mittag-Leffler functions with two or three parameters -- 4.Generalized Mittag-Leffler functions -- 5.Mittag-Leffler functions and solution to fractional order equations -- 6.Applications to deterministic models -- 7.Applications to stochastic models -- Appendices -- A. Euler Gamma and Beta-functions -- B. Entire functions -- C. Integral transforms -- D. Mellin-Barnes integral -- E. Elements of fractional calculus -- F. Higher transcendental functions -- References. |
| Record Nr. | UNINA-9910299992403321 |
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Gorenflo Rudolf
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| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Nonlocal and fractional operators / / Luisa Beghin, Francesco Mainardi, Roberto Garrappa, editors
| Nonlocal and fractional operators / / Luisa Beghin, Francesco Mainardi, Roberto Garrappa, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (314 pages) |
| Disciplina | 515 |
| Collana | SEMA SIMAI Springer Series |
| Soggetto topico |
Fractional calculus
Operator theory Càlcul fraccional Teoria d'operadors |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-69236-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910494562603321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Nonlocal and fractional operators / / Luisa Beghin, Francesco Mainardi, Roberto Garrappa, editors
| Nonlocal and fractional operators / / Luisa Beghin, Francesco Mainardi, Roberto Garrappa, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (314 pages) |
| Disciplina | 515 |
| Collana | SEMA SIMAI Springer Series |
| Soggetto topico |
Fractional calculus
Operator theory Càlcul fraccional Teoria d'operadors |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-69236-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNISA-996466404903316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Special Functions with Applications to Mathematical Physics / / edited by Francesco Mainardi
| Special Functions with Applications to Mathematical Physics / / edited by Francesco Mainardi |
| Pubbl/distr/stampa | Basel : , : MDPI, , 2023 |
| Descrizione fisica | 1 online resource (438 pages) |
| Disciplina | 530.15 |
| Soggetto topico | Mathematical physics |
| ISBN | 3-0365-6991-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910683370603321 |
| Basel : , : MDPI, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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