| Pubbl/distr/stampa |
Cham, Switzerland : , : Springer, , [2022]
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| Descrizione fisica |
1 online resource (268 pages) : illustrations (chiefly color)
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| Disciplina |
515.83
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| Collana |
Lecture notes in networks and systems
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| Soggetto topico |
Fractional calculus
Fractional differential equations
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| ISBN |
3-031-04383-9
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| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
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| Nota di contenuto |
Intro -- Preface -- Contents -- Some Proposals for a Renewal in the Field of Fractional Behaviour Analysis and Modelling -- 1 Introduction -- 2 Fractional Order Models and Associated Drawbacks -- 3 Some New Kernels -- 3.1 Kernels 1 ( t ) -- 3.2 Kernel 2 ( t ) -- 3.3 Kernel 3 ( t ) -- 3.4 Kernel 4 ( t ) -- 4 Volterra Equations -- 5 Other Alternative Models to Capture Power Law Type Behaviours -- 5.1 Distributed Time Delay Systems -- 5.2 Nonlinear Models -- 5.3 Partial Differential Equations (Diffusion Equations) with Spatially Variable Coefficients -- 6 Conclusion -- References -- Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used -- 1 Introduction -- 2 Problem Analysis with Caputo's Definition -- 3 Analysis with Other Definitions -- 3.1 The Riemann-Liouville Definition -- 3.2 The Grünwald-Letnikov Definition -- 4 Need to Take into Account All of the Model Past -- 5 Conclusion -- References -- The Complex Order Fractional Derivatives and Systems are Non Hermitian -- 1 Introduction -- 2 The Hermitian Property of Real Order Fractional Derivatives -- 3 Complex Order Derivatives -- 3.1 Non Hermitian Character -- 3.2 Using the Hilbert Transform -- 4 The Hermitian Part -- References -- Transient Regime of Fractional RLC Circuit -- 1 Introduction -- 2 Model Formulation and Analytical Solution -- 3 Conclusion -- References -- Modelling Cardiovascular Diseases with Fractional-Order Derivatives -- 1 Introduction -- 2 Description of the Cardiovascular System -- 3 Fractional-Order Model of the Cardiovascular System -- 4 Modelling of Pathologies -- 5 Conclusions -- References -- Frequency Domain Modeling of an IPMC-Based Artificial Eukaryotic Flagellum Swimming Robot -- 1 Introduction -- 2 Modeling of IPMC Actuators -- 3 Experiments -- 3.1 Swimming Robot -- 3.2 Set-up.
3.3 Measured Frequency Responses -- 4 Identified Dynamic Models for Control -- 5 Conclusions -- References -- Accuracy Analysis of Approximated Fractional Order Transfer Function with Pole and Zero -- 1 Introduction -- 2 Preliminaries-The Charef Approximation -- 3 The Considered Transfer Function with Zero and Pole -- 4 The Proposed Approximation of the Transfer Function -- 5 Examples -- 5.1 Example 1 -- 5.2 Example 2 -- 5.3 Example 3 -- 6 Final Conclusions -- References -- Fractional Order Models Are Doubly Infinite Dimensional Models and Thus of Infinite Memory: Consequences on Initialization and Some Solutions -- 1 Introduction -- 2 A Physical and Systemic Analysis of Fractional Models -- 2.1 Models Definition -- 2.2 Poles and Time Constants Distribution and Infinite Memory -- 2.3 Spatial Definition and Infinite Memory -- 3 Other Modelling Solutions -- 3.1 Kernels with Limited Memory -- 3.2 Volterra Integro-Differential Equations -- 3.3 Time Delay Models -- 3.4 Nonlinear Models -- 3.5 Time Varying Models -- 3.6 Diffusion Equation with Spatially Variable Coefficients -- 4 Conclusion -- References -- Stability Analysis of COVID-19 via a Fractional Order Mathematical Model -- 1 Introduction and Preliminaries -- 2 Description of the SEIR Covid-19 Model -- 3 Stability Analysis of the Model -- 3.1 Local Stability Analysis -- 4 Numerical Simulation and Discussion -- 5 Concluding Remarks -- References -- Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior -- 1 Introduction -- 2 Evidence of the Fractionnal Asymptotic Behavior for Some Fractal Surfaces -- 3 Power-Law Non Linear Dynamical Modeling -- 4 Conclusion -- References -- Vectorization Calculation Method of the Fractional-Order Mem-Elements -- 1 Introduction -- 2 Vectorization of Fractional-Order Memristor, Meminductor and Memcapacitor.
2.1 HP Model and Fractional Order Mem-Elements -- 2.2 The Vectorization of Fractional Order Mem-Elements -- 2.3 Different Kinds of Mem-Elements Superposition -- 3 Conclusion -- References -- Which Kind of Fractional Partial Differential Equations Has Solution with Exponential Asymptotics? -- 1 Introduction -- 2 Exponential Asymptotics -- 3 Conclusion -- References -- Detection of a Fractal Element with Complex-Conjugated Power-Law Exponents in Living Systems: Analysis of the Temporal Evolution of Impedance Measurements in the Unblown Bud Plumeria Flower (Frangipani Plumeria) -- 1 The Theory of the Branching System in the Frequency Domain -- 2 The Basic Plots Demonstrating the Fit of the Found Functions Eq. (7, 8) to the Measured Data -- 3 The Results Obtained -- 4 Mathematical Appendix -- 4.1 How to Obtain the Functional Eq. (4)? -- 4.2 How to Obtain the Solution (6) of the Functional Eq. (4)? -- References -- Prabhakar Discrete-Time Generalization of the Time-Fractional Poisson Process and Related Random Walks -- 1 Introduction -- 2 The Prabahakar Discrete-Time Counting Process -- 3 Prabhakar Discrete Time Random Walk Model -- 4 Conclusions -- References -- A Temporal Second-Order Scheme for Time Fractional Mixed Diffusion and Wave Equation with an Initial Singularity -- 1 Model Problem -- 2 Crank-Nicolson Formulae and Error Analyses -- 2.1 C-N Formulae to Approximate Fractional Operators -- 2.2 Error Analyses -- 3 A Numerical Scheme on Graded Meshes -- 4 Numerical Examples -- 5 Conclusion -- References -- Optimized Current and Speed Fractional-Order PID Control in Electrical Drives -- 1 Introduction -- 2 Mathematical Preliminaries -- 3 Controllers Optimization -- 4 Solving the Optimization Problem -- 5 Simulation Results -- 6 Conclusion -- References -- Operational Calculus with Applications to Generalized Two-Sided Fractional Derivative.
1 Introduction -- 2 Generalized Two-Sided Fractional Derivative -- 3 Operational Calculus -- 4 Illustrative Examples -- 5 Conclusions -- References -- A Remark on the Memory Property of Fractional Difference Operators -- 1 Introduction and Preliminaries -- 2 Main Results -- 3 Conclusion -- References -- Mikusiński's Operational Calculus Applied in General Classes of Fractional Calculus -- 1 Introduction -- 2 The Riemann-Liouville and Caputo Settings -- 2.1 Informal Description -- 2.2 Formal Analysis -- 3 The General Setting of Fractional Calculus with Respect to Functions -- 4 Other Generalisations and Extensions -- References -- Control of All Axis in 3D Crane Using FOPID Controllers Optimized with GWO Algorithm -- 1 Introduction -- 2 FOPID Controller -- 3 Grey Wolf Optimizer -- 4 Mathematical Model of the 3D Crane -- 5 Implementation of Simulation -- 6 Results of Simulation -- 7 Conclusion -- References -- Axial Stabilizing CRONE Controller of an Active Magnetic Bearing with Strong Performance and Control-Effort Specifications -- 1 Introduction -- 2 Description of the Axial Rotor Dynamic and the AMB Control Loop -- 2.1 System Short Description -- 2.2 AMB Modelling -- 2.3 Dynamic of the Axial Deviation Measurement -- 2.4 Simulator Test Bench -- 3 Design of the Control-System -- 3.1 Linear Model Description -- 3.2 CRONE Design of a Robust Feedback Digital Controller -- 3.3 Optimal Loop Shaping of the CRONE Open Loop Nominal Transfer Function -- 3.4 Rational Approximation of the Fractional Order Controller -- 4 Simulation Assessments -- 5 Conclusion -- References -- Matsuda Method Adapted to Identify Fractional Order Transfer Functions -- 1 Introduction -- 2 The Original Matsuda Method -- 2.1 Continued Fractions -- 2.2 Identification -- 3 Identifying Implicit Fractional Order Transfer Functions.
4 Identifying Explicit Commensurable Fractional Order Transfer Functions -- 5 Examples of Application -- 5.1 Metaheuristics -- 5.2 Identifying Filters with One Pole -- 5.3 Identifying Filters with Two Poles -- 5.4 General Fractional Order Filter Design -- 6 Discussion and Conclusions -- References -- An Existence Result for a Fractional Integral Boundary Value Problem of Mixed Type with Impulses -- 1 The Impulsive Problem -- 1.1 Preliminaries -- 2 Main Result -- 3 Example -- References -- Pattern Formation in Activator-Inhibitor Fractional Reaction-Diffusion Systems -- 1 Generalized Basic Two-Component Activator-Inhibitor System -- 2 Linear Stability Analysis -- 2.1 Standard Reaction-Diffusion System -- 2.2 Space-Fractional Reaction-Diffusion System -- 2.3 Time-Fractional Reaction-Diffusion System -- 3 Pattern Formation in Fractional RDS -- 3.1 Basic Activator-Inhibitor Mathematical Models -- 3.2 Complex Spatio-Temporal Dynamics in Fractional RDS -- References -- Stability Results for Two-Term Fractional-Order Difference Equations -- 1 Introduction -- 2 Preliminaries -- 3 Stability Results for Two-Term Fractional-Order Difference Equations -- 4 Fractional-Order Dependent Stability Results -- 5 Conclusions -- References -- Global Thermal Modeling of Lung Heat Transfer with Blood Perfusion -- 1 Introduction -- 2 Two-Port Network Models -- 2.1 Classic Two-Port Network -- 2.2 Bio-heat Two-Port Network -- 2.3 T Circuit -- 3 Lung Global Model -- 4 Simulations and Results -- 5 Conclusions -- References -- Finite Difference Schemes with Non-uniform Time Meshes for Distributed-Order Diffusion Equations -- 1 Introduction -- 2 Finite Difference Scheme -- 3 Numerical Results -- 4 Conclusions -- References -- CRONE Controller Synthesis Improvement by an Additional Feedback -- 1 Introduction -- 2 Mathematical Preliminaries.
2.1 Fractional Integral and Fractional Derivative.
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| Record Nr. | UNINA-9910568238803321 |
Info
Numerical methods for fractional calculus / / Changpin Li, Department of Mathematics, Shanghai University, China; Fanhai Zeng, Department of Mathematics, Shanghai University, China
