Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators

[1]  H. Kaufman,et al.  Table of Laplace transforms , 1966 .

[2]  On Self-Consistent Operators With Application to Operators of Fractional Order , 2009 .

[3]  Alain Oustaloup,et al.  On Observability of Fractional Order Systems , 2009 .

[4]  Alain Oustaloup,et al.  State variables and transients of fractional order differential systems , 2012, Comput. Math. Appl..

[5]  Carl F. Lorenzo,et al.  Initialization in fractional order systems , 2001, 2001 European Control Conference (ECC).

[6]  Carl F. Lorenzo,et al.  Initialization of Fractional Differential Equations: Theory and Application , 2007 .

[7]  T. Hartley,et al.  Initialization, conceptualization, and application in the generalized (fractional) calculus. , 2007, Critical reviews in biomedical engineering.

[8]  T. Hartley,et al.  Application of Incomplete Gamma Functions to the Initialization of Fractional-Order Systems , 2007 .

[9]  T. Hartley,et al.  The Vertical Linear Fractional Initialization Problem , 1999 .

[10]  Carl F. Lorenzo,et al.  Initialization of Fractional Differential Equations: Background and Theory , 2007 .

[11]  P. Coirault,et al.  Parameter estimation of fractional systems application to heat transfer , 2001, 2001 European Control Conference (ECC).

[12]  Alain Oustaloup,et al.  Transients of fractional-order integrator and derivatives , 2012, Signal Image Video Process..

[13]  J. L. Adams,et al.  The inverted initialization problem for fractional-order derivatives , 2009 .

[14]  Carl F. Lorenzo,et al.  Variable Order and Distributed Order Fractional Operators , 2002 .

[15]  Nobuyuki Shimizu,et al.  Role of Prehistories in the Initial Value Problems of Fractional Viscoelastic Equations , 2004 .

[16]  Régis Ouvrard,et al.  Parameter Estimation of Fractional Systems: Application to the Modeling of a Lead-Acid Battery , 2000 .

[17]  Carl F. Lorenzo,et al.  Initialized Fractional Calculus , 2000 .

[18]  Alain Oustaloup,et al.  Fractional integration: A comparative analysis of fractional integrators , 2011, Eighth International Multi-Conference on Systems, Signals & Devices.

[19]  Amel Benchellal,et al.  Modélisation des interfaces de diffusion à l'aide d'opérateurs d' intégration fractionnaires , 2008 .

[20]  Christophe Farges,et al.  On Observability and Pseudo State Estimation of Fractional Order Systems , 2012, Eur. J. Control.

[21]  Carl F. Lorenzo,et al.  Initialization Issues of the Caputo Fractional Derivative , 2005 .

[22]  T. Hartley,et al.  Dynamics and Control of Initialized Fractional-Order Systems , 2002 .

[23]  N. Maamri,et al.  State space modeling of fractional differential equations and the initial condition problem , 2009, 2009 6th International Multi-Conference on Systems, Signals and Devices.

[24]  Alain Oustaloup,et al.  Automatic initialization of the Caputo fractional derivative , 2011, IEEE Conference on Decision and Control and European Control Conference.

[25]  Z. Wang,et al.  Initialized fractional differential equations with Riemann-Liouville fractional-order derivative , 2011 .

[26]  Manuel Duarte Ortigueira,et al.  On the initial conditions in continuous-time fractional linear systems , 2003, Signal Process..

[27]  Jean-Claude Trigeassou,et al.  Initial conditions and initialization of linear fractional differential equations , 2011, Signal Process..

[28]  Carl F. Lorenzo,et al.  Control of Initialized Fractional-Order Systems , 2002 .

[29]  Carl F. Lorenzo,et al.  The Initialization Response of Multi-Term Linear Fractional-Order Systems With Constant History Functions , 2011 .

[30]  Thierry Poinot,et al.  A method for modelling and simulation of fractional systems , 2003, Signal Process..

[31]  Carl F. Lorenzo,et al.  THE INITIALIZATION RESPONSE OF LINEAR FRACTIONAL-ORDER SYSTEMS WITH CONSTANT HISTORY FUNCTION , 2009 .

[32]  Alain Oustaloup,et al.  How to impose physically coherent initial conditions to a fractional system , 2010 .

[33]  Carl F. Lorenzo,et al.  AN EXPERIMENTAL VALIDATION OF THE TIME-VARYING INITIALIZATION RESPONSE IN FRACTIONAL-ORDER SYSTEMS , 2011 .

[34]  Thierry Poinot,et al.  PARAMETER ESTIMATION OF FRACTIONAL MODELS: APPLICATION TO THE MODELING OF DIFFUSIVE SYSTEMS , 2002 .

[35]  Alain Oustaloup,et al.  Initialization of Riemann-Liouville and Caputo Fractional Derivatives , 2011 .

[36]  T. Hartley,et al.  Initialization of Fractional-Order Operators and Fractional Differential Equations , 2008 .

[37]  Carl F. Lorenzo,et al.  Time-Varying Initialization and Laplace Transform of the Caputo Derivative: With Order Between Zero and One , 2011 .

[38]  Alain Oustaloup,et al.  A Lyapunov approach to the stability of fractional differential equations , 2009, Signal Process..

[39]  Alain Oustaloup,et al.  On a representation of fractional order systems: interests for the Initial Condition Problem , 2008 .

[40]  A. Oustaloup,et al.  Modeling and identification of a non integer order system , 1999, 1999 European Control Conference (ECC).