A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay

[1]  X. Pei,et al.  A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics , 2018, Bulletin of Engineering Geology and the Environment.

[2]  Behrouz Parsa Moghaddam,et al.  An integro quadratic spline approach for a class of variable-order fractional initial value problems , 2017 .

[3]  Eric A. Butcher,et al.  Efficient modified Chebyshev differentiation matrices for fractional differential equations , 2017, Commun. Nonlinear Sci. Numer. Simul..

[4]  António M. Lopes,et al.  A fractional perspective on the trajectory control of redundant and hyper-redundant robot manipulators , 2017 .

[5]  José António Tenreiro Machado,et al.  Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications , 2017, J. Sci. Comput..

[6]  M. Sen,et al.  The existence and numerical solution for a k-dimensional system of multi-term fractional integro-differential equations , 2017 .

[7]  Morad Nazari,et al.  Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation , 2017 .

[8]  Behrouz Parsa Moghaddam,et al.  Modified finite difference method for solving fractional delay differential equations , 2017 .

[9]  António M. Lopes,et al.  Application of Fractional Techniques in the Analysis of Forest Fires , 2016 .

[10]  J. Machado,et al.  A new fractional operator of variable order: Application in the description of anomalous diffusion , 2016, 1611.09200.

[11]  J. A. Tenreiro Machado,et al.  An Extended Predictor–Corrector Algorithm for Variable-Order Fractional Delay Differential Equations , 2016 .

[12]  Eric A. Butcher,et al.  Fractional Delayed Control Design for Linear Periodic Systems , 2016 .

[13]  Morad Nazari,et al.  The spectral parameter estimation method for parameter identification of linear fractional order systems , 2016, 2016 American Control Conference (ACC).

[14]  J. K. Liu,et al.  Steady state response analysis for fractional dynamic systems based on memory-free principle and harmonic balancing , 2016 .

[15]  Abhishek Dutta,et al.  Tuning algorithms for fractional order internal model controllers for time delay processes , 2016, Int. J. Control.

[16]  L. Hong,et al.  Global dynamics of fractional-order systems with an extended generalized cell mapping method , 2016 .

[17]  Nagarajan Sukavanam,et al.  Sensitivity analysis of nonlinear fractional order control systems with state delay , 2016, Int. J. Comput. Math..

[18]  S. Bhalekar,et al.  Solving Fractional Delay Differential Equations: A New Approach , 2015 .

[19]  Behrouz Parsa Moghaddam,et al.  A novel matrix approach to fractional finite difference for solving models based on nonlinear fractional delay differential equations , 2014 .

[20]  M. Sen.  On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics , 2014 .

[21]  Neville J. Ford,et al.  Analysis and numerical methods for fractional differential equations with delay , 2013, J. Comput. Appl. Math..

[22]  J. Tenreiro Machado,et al.  Science metrics on fractional calculus development since 1966 , 2013 .

[23]  Carlos F.M. Coimbra,et al.  On the variable order dynamics of the nonlinear wake caused by a sedimenting particle , 2011 .

[24]  YangQuan Chen,et al.  A Physical experimental study of variable-order fractional integrator and differentiator , 2011 .

[25]  W. Chen,et al.  A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems , 2011 .

[26]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[27]  M. De la Sen,et al.  About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory , 2011 .

[28]  Hal L. Smith,et al.  An introduction to delay differential equations with applications to the life sciences / Hal Smith , 2010 .

[29]  Y. Chen,et al.  Variable-order fractional differential operators in anomalous diffusion modeling , 2009 .

[30]  Z. H. Wang,et al.  The optimal form of the fractional-order difference feedbacks in enhancing the stability of a sdof vibration system , 2009 .

[31]  S. Momani,et al.  An efficient method for solving systems of fractional integro-differential equations , 2006, Comput. Math. Appl..

[32]  Marc Weilbeer,et al.  Efficient Numerical Methods for Fractional Differential Equations and their Analytical Background , 2005 .

[33]  Carlos F.M. Coimbra,et al.  The variable viscoelasticity oscillator , 2005 .

[34]  Carlos F.M. Coimbra,et al.  Mechanics with variable‐order differential operators , 2003 .

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

[36]  Dean T. Mook,et al.  Cargo Pendulation Reduction on Ship-Mounted Cranes Via Boom-Luff Angle Actuation , 2001 .

[37]  Ali H. Nayfeh,et al.  Delayed Position-Feedback Controller for the Reduction of Payload Pendulations of Rotary Cranes , 2001 .

[38]  Dov Ingman,et al.  Constitutive Dynamic-Order Model for Nonlinear Contact Phenomena , 2000 .

[39]  Stefan Samko,et al.  Fractional integration and differentiation of variable order , 1995 .

[40]  Wook Hyun Kwon,et al.  Performance improvement using time delays in multivariable controller design , 1990 .

[41]  R. D. Johnston,et al.  Exploitation of time delays for improved process control , 1988 .

[42]  Z. Bien,et al.  Use of time-delay actions in the controller design , 1980 .

[43]  Il Hong Suh,et al.  Proportional minus delay controller , 1979 .

[44]  Morad Nazari,et al.  Stability and Control of Fractional Periodic Time-Delayed Systems , 2017 .

[45]  José António Tenreiro Machado,et al.  SM-Algorithms for Approximating the Variable-Order Fractional Derivative of High Order , 2017, Fundam. Informaticae.

[46]  Y. Xiaojun,et al.  Advanced Local Fractional Calculus and Its Applications , 2012 .

[47]  Yang Xiao-Jun.  Local Fractional Functional Analysis and Its Applications , 2011 .

[48]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[49]  I. Podlubny.  Fractional-Order Systems and -Controllers , 1999 .

[50]  J. Machado.  Fractional-order derivative approximations in discrete-time control systems , 1998 .

[51]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .