Topics: Discrete systems , Dynamic systems , Dynamics (Mechanics) , Phase space , Variational principles , Variational techniques , Nonlinear dynamical systems , Physics , Momentum

Application of Incomplete Gamma Functions to the Initialization of Fractional-Order Systems

Tom T. Hartley, Carl F. Lorenzo

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021103. doi: https://doi.org/10.1115/1.2833480

Abstract

View articletitled, Application of Incomplete Gamma Functions to the Initialization of Fractional-Order Systems

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Topics: Differential equations , Gamma functions , Laplace transforms

On the Differential Geometry of Flows in Nonlinear Dynamical Systems

Albert C. J. Luo

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021104. doi: https://doi.org/10.1115/1.2835060

Abstract

View articletitled, On the Differential Geometry of Flows in Nonlinear Dynamical Systems

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Topics: Flow (Dynamics) , Dynamic systems

Modeling

Fractional Dynamics: A Statistical Perspective

J. A. Tenreiro Machado, Alexandra Galhano

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021201. doi: https://doi.org/10.1115/1.2833481

Abstract

View articletitled, Fractional Dynamics: A Statistical Perspective

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Topics: Dynamics (Mechanics) , Simulation , Modeling

Formulation of A State Equation Including Fractional-Order State Vectors

Masaharu Kuroda

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021202. doi: https://doi.org/10.1115/1.2833482

Abstract

View articletitled, Formulation of A State Equation Including Fractional-Order State Vectors

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Topics: Control engineering , Control equipment , Control systems , Control theory , Design , Dynamics (Mechanics) , Robust control

Fractional Dynamics in Mechanical Manipulation

Miguel F. M. Lima, J. A. Tenreiro Machado, Manuel Crisóstomo

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021203. doi: https://doi.org/10.1115/1.2833488

Abstract

View articletitled, Fractional Dynamics in Mechanical Manipulation

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Topics: Containers , Dynamics (Mechanics) , Robots , Signals , Vibration , Sensors , Fourier transforms , Manipulators

Fractional Optimal Control of a Distributed System Using Eigenfunctions

Om P. Agrawal

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021204. doi: https://doi.org/10.1115/1.2833873

Abstract

View articletitled, Fractional Optimal Control of a Distributed System Using Eigenfunctions

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Topics: Eigenfunctions , Optimal control

Dynamics of a Duffing Oscillator With Two Time Delays in Feedback Control Under Narrow-Band Random Excitation

Yanfei Jin, Haiyan Hu

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021205. doi: https://doi.org/10.1115/1.2833890

Abstract

View articletitled, Dynamics of a Duffing Oscillator With Two Time Delays in Feedback Control Under Narrow-Band Random Excitation

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Topics: Delays , Feedback , Resonance , Steady state , Random excitation , Stability

Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

Meng Xu, Ziyou Gao

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021206. doi: https://doi.org/10.1115/1.2833905

Abstract

View articletitled, Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

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Topics: Dimensions , Flow (Dynamics) , Traffic , Fractals , Chaos , Density , Dynamic systems

Identifying a Transfer Function From a Frequency Response

Duarte Valério, Manuel Duarte Ortigueira, José Sá da Costa

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021207. doi: https://doi.org/10.1115/1.2833906

Abstract

View articletitled, Identifying a Transfer Function From a Frequency Response

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Topics: Frequency response , Noise (Sound) , Transfer functions , Waves , Algorithms , Engineering prototypes , Ocean waves

Implementation

Microelectronic Implementations of Fractional-Order Integrodifferential Operators

Guillermo E. Santamaría, José V. Valverde, Raquel Pérez-Aloe, Blas M. Vinagre

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021301. doi: https://doi.org/10.1115/1.2833907

Abstract

View articletitled, Microelectronic Implementations of Fractional-Order Integrodifferential Operators

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Topics: Capacitors , Circuits , Design , Gates (Closures) , Transfer functions , Microelectronic devices , Poles (Building) , Approximation

Field Programmable Analog Array Implementation of Noninteger Order $P I^{λ} D^{μ}$ Controller

Riccardo Caponetto, Giovanni Dongola

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021302. doi: https://doi.org/10.1115/1.2833908

Abstract

View articletitled, Field Programmable Analog Array Implementation of Noninteger Order <span class="inline-formula no-formula-id"><span class="mathFormula"></span><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>P</mi><msup><mi>I</mi><mi>λ</mi></msup><msup><mi>D</mi><mi>μ</mi></msup></mrow></math></span> Controller

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Topics: Control equipment , Signals , Poles (Building) , Transfer functions , Approximation

Modeling of Electrochemical Double Layer Capacitors by Means of Fractional Impedance

Rodolfo Martín, Jose J. Quintana, Alejandro Ramos, Ignacio de la Nuez

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021303. doi: https://doi.org/10.1115/1.2833909

Abstract

View articletitled, Modeling of Electrochemical Double Layer Capacitors by Means of Fractional Impedance

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Topics: Capacitors , Modeling , Ultracapacitors

Control

Advances in System Identification Using Fractional Models

Rachid Malti, Stephane Victor, Alain Oustaloup

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021401. doi: https://doi.org/10.1115/1.2833910

Abstract

View articletitled, Advances in System Identification Using Fractional Models

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Topics: Errors , Simulation , Thermal systems

Finite-Time Controllability of Fractional-Order Systems

Jay L. Adams, Tom T. Hartley

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021402. doi: https://doi.org/10.1115/1.2833919

Abstract

View articletitled, Finite-Time Controllability of Fractional-Order Systems

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Topics: Optimal control , Theorems (Mathematics) , Concretes

Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers

YangQuan Chen, Tripti Bhaskaran, Dingyü Xue

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021403. doi: https://doi.org/10.1115/1.2833934

Abstract

View articletitled, Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers

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Topics: Control equipment , Delays , Optimization

Fractional Order Filter Enhanced LQR for Seismic Protection of Civil Structures

Abdollah Shafieezadeh, Keri Ryan, YangQuan Chen

J. Comput. Nonlinear Dynam. January 2008, 3(2): 021404. doi: https://doi.org/10.1115/1.2833947

Abstract

View articletitled, Fractional Order Filter Enhanced LQR for Seismic Protection of Civil Structures

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Topics: Control equipment , Earthquakes , Filters , Optimization , Weight (Mass) , Algorithms , Robust control , Approximation , Simulation results

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Editorial

Special Issue on “Discontinuous and Fractional Dynamical Systems”

Research Papers

Mathematical Theory

Initialization of Fractional-Order Operators and Fractional Differential Equations

Fractional Constrained Systems and Caputo Derivatives

Application of Incomplete Gamma Functions to the Initialization of Fractional-Order Systems

On the Differential Geometry of Flows in Nonlinear Dynamical Systems

Modeling

Fractional Dynamics: A Statistical Perspective

Formulation of A State Equation Including Fractional-Order State Vectors

Fractional Dynamics in Mechanical Manipulation

Fractional Optimal Control of a Distributed System Using Eigenfunctions

Dynamics of a Duffing Oscillator With Two Time Delays in Feedback Control Under Narrow-Band Random Excitation

Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

Identifying a Transfer Function From a Frequency Response

Implementation

Microelectronic Implementations of Fractional-Order Integrodifferential Operators

Field Programmable Analog Array Implementation of Noninteger Order $P I^{λ} D^{μ}$ Controller

Modeling of Electrochemical Double Layer Capacitors by Means of Fractional Impedance

Control

Advances in System Identification Using Fractional Models

Finite-Time Controllability of Fractional-Order Systems

Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers

Fractional Order Filter Enhanced LQR for Seismic Protection of Civil Structures

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