Ebook: Fractional Dynamics and Control

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

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Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

• Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues

• Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation

• Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics

• Develops new methods for control and synchronization of factional dynamical systems

Fractional Dynamics andControl is an ideal book for scholars, researchers and advanced technical members of industrial laboratory facilities, for developing new tools and products in the field of nonlinear dynamics and control.

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Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

• Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues

• Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation

• Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics

• Develops new methods for control and synchronization of factional dynamical systems

Fractional Dynamics andControl is an ideal book for scholars, researchers and advanced technical members of industrial laboratory facilities, for developing new tools and products in the field of nonlinear dynamics and control.

Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
A Formulation and Numerical Scheme for Fractional Optimal Control of Cylindrical Structures Subjected to General Initial Conditions....Pages 3-17
Neural Network-Assisted PI?D? Control....Pages 19-31
Application of Backstepping Control Technique to Fractional Order Dynamic Systems....Pages 33-47
Parameter Tuning of a Fractional-Order PI Controller Using the ITAE Criteria....Pages 49-57
A Fractional Model Predictive Control for Fractional Order Systems....Pages 59-71
Stabilization of Fractional Order Unified Chaotic Systems via Linear State Feedback Controller....Pages 73-83
Front Matter....Pages 85-94
Fractional Variational Calculus for Non-differentiable Functions....Pages 95-95
Fractional Euler–Lagrange Differential Equations via Caputo Derivatives....Pages 97-108
Strict Stability of Fractional Perturbed Systems in Terms of Two Measures....Pages 109-118
Initial Time Difference Strict Stability of Fractional Dynamic Systems....Pages 119-132
A Fractional Order Dynamical Trajectory Approach for Optimization Problem with HPM....Pages 133-144
Front Matter....Pages 145-155
On the Hadamard Type Fractional Differential System....Pages 157-157
Robust Synchronization and Parameter Identification of a Unified Fractional-Order Chaotic System....Pages 159-171
Fractional Cauchy Problems on Bounded Domains: Survey of Recent Results....Pages 173-184
Fractional Analogous Models in Mechanics and Gravity Theories....Pages 185-198
Schr?dinger Equation in Fractional Space....Pages 199-207
Solutions of Wave Equation in Fractional Dimensional Space....Pages 209-215
Fractional Exact Solutions and Solitons in Gravity....Pages 217-228
Front Matter....Pages 229-236
Front Propagation in an Autocatalytic Reaction-Subdiffusion System....Pages 237-237
Front Matter....Pages 239-247
Numerical Solution of a Two-Dimensional Anomalous Diffusion Problem....Pages 237-237
Analyzing Anomalous Diffusion in NMR Using a Distribution of Rate Constants....Pages 249-261
Using Fractional Derivatives to Generalize the Hodgkin–Huxley Model....Pages 263-274
An Application of Fractional Calculus to Dielectric Relaxation Processes....Pages 275-282
Fractional Wave Equation for Dielectric Medium with Havriliak–Negami Response....Pages 283-291
Back Matter....Pages 293-301
....Pages 303-309