Initial Conditions and Initialization of Fractional Systems

[1]  I. Podlubny,et al.  Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives , 2005, math-ph/0512028.

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

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

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

[5]  Christophe Farges,et al.  Fractional systems state space description: some wrong ideas and proposed solutions , 2014 .

[6]  Charles A. Desoer,et al.  Linear System Theory: The State Space Approach , 2008 .

[7]  I. Podlubny Fractional differential equations , 1998 .

[8]  Zaihua Wang,et al.  Correcting the initialization of models with fractional derivatives via history-dependent conditions , 2016 .

[9]  R. E. Kalman,et al.  On the general theory of control systems , 1959 .

[10]  Gérard Montseny,et al.  Diffusive representation of pseudo-differential time-operators , 1998 .

[11]  Christophe Farges,et al.  Approximation of a fractional order model by an integer order model: a new approach taking into account approximation error as an uncertainty , 2016 .

[12]  Nezha Maamri,et al.  Physical interpretation and initialization of the fractional integrator , 2014, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014.

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

[14]  José António Tenreiro Machado,et al.  Integer/fractional decomposition of the impulse response of fractional linear systems , 2015, Signal Process..

[15]  Hayley H. Shen,et al.  Modeling ocean wave propagation under sea ice covers , 2015 .

[16]  Thomas Kailath,et al.  Linear Systems , 1980 .

[17]  Alain Oustaloup,et al.  The infinite state approach: Origin and necessity , 2013, Comput. Math. Appl..

[18]  Don Patinkin On the General Theory , 1989 .

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

[20]  J. A. Tenreiro Machado,et al.  Numerical analysis of the initial conditions in fractional systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

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

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

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

[24]  Trigeassou Jean-Claude,et al.  The Caputo Derivative And The Infinite State Approach , 2013 .

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

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

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

[28]  Alain Oustaloup,et al.  Lyapunov stability of fractional order systems: The two derivatives case , 2014, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014.

[29]  Carl F. Lorenzo,et al.  Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators , 2013 .