Some stability properties related to initial time difference for Caputo fractional differential equations

Abstract Lipschitz stability and Mittag-Leffler stability with initial time difference for nonlinear nonautonomous Caputo fractional differential equation are defined and studied using Lyapunov like functions. Some sufficient conditions are obtained. The fractional order extension of comparison principles via scalar fractional differential equations with a parameter is employed. The relation between both types of stability is discussed theoretically and it is illustrated with examples.

[1]  D. O’Regan,et al.  Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions , 2017 .

[2]  Ravi P. Agarwal,et al.  Stability with Initial Time Difference of Caputo Fractional Differential Equations by Lyapunov Functions , 2017 .

[3]  Ravi P. Agarwal,et al.  Practical stability with respect to initial time difference for Caputo fractional differential equations , 2017, Commun. Nonlinear Sci. Numer. Simul..

[4]  Liancun Zheng,et al.  Existence and uniqueness of global solutions of caputo-type fractional differential equations , 2016 .

[5]  Donal O’Regan,et al.  A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations , 2016 .

[6]  Donal O’Regan,et al.  Stability of Caputo fractional differential equations by Lyapunov functions , 2015 .

[7]  S. Abbas,et al.  New Stability Results for Partial Fractional Differential Inclusions with Not Instantaneous Impulses , 2015 .

[8]  S. Hristova.  STABILITY WITH RESPECT TO INITIAL TIME DIFFERENCE FOR GENERALIZED DELAY DIFFERENTIAL EQUATIONS , 2015 .

[9]  A. Xiao,et al.  Dissipativity and Stability Analysis for Fractional Functional Differential Equations , 2015 .

[10]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[11]  Coșkun Yakar,et al.  Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference , 2014, TheScientificWorldJournal.

[12]  Ivanka M. Stamova,et al.  Lipschitz stability criteria for functional differential systems of fractional order , 2013 .

[13]  J. Vasundhara Devi,et al.  Variational Lyapunov method for fractional differential equations , 2012, Comput. Math. Appl..

[14]  Zhuang Jiao,et al.  Stability analysis of fractional-order systems with double noncommensurate orders for matrix case , 2011 .

[15]  S. Das.  Functional Fractional Calculus , 2011 .

[16]  Dumitru Baleanu,et al.  On the global existence of solutions to a class of fractional differential equations , 2010, Comput. Math. Appl..

[17]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[18]  Coşkun Yakar.  Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference , 2010 .

[19]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[20]  LIPSCHITZ STABILITY AND EXPONENTIAL ASYMPTOTIC STABILITY IN PERTURBED SYSTEMS , 2008 .

[21]  S. Leela,et al.  LYAPUNOV THEORY FOR FRACTIONAL DIFFERENTIAL EQUATIONS , 2008 .

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

[23]  Saber Elaydi,et al.  Lipschitz stability of nonlinear systems of differential equations , 1986 .