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V. Lakshmikantham, R. Mohapatra (2001)
Strict stability of differential equationsNonlinear Analysis-theory Methods & Applications, 46
(1999)
Stability criteria for solutions of differential equations relative to initial time difference
D. Baleanu, O. Mustafa (2010)
On the global existence of solutions to a class of fractional differential equationsComput. Math. Appl., 59
R. Agarwal, D. O’Regan, S. Hristova (2015)
Stability of Caputo fractional differential equations by Lyapunov functionsApplications of Mathematics, 60
S. Leela, M. Sambandham (2008)
LYAPUNOV THEORY FOR FRACTIONAL DIFFERENTIAL EQUATIONS
R. Metzler, J. Klafter (2000)
The random walk's guide to anomalous diffusion: a fractional dynamics approachPhysics Reports, 339
Yan Li, Y. Chen, I. Podlubny (2010)
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stabilityComput. Math. Appl., 59
J. Devi, F. McRae, Z. Drici (2012)
Variational Lyapunov method for fractional differential equationsComput. Math. Appl., 64
S. Das (2011)
Functional Fractional Calculus
R. Ashurov, A. Cabada, B. Turmetov (2016)
Operator Method for Construction of Solutions of Linear Fractional Differential Equations with Constant CoefficientsFractional Calculus and Applied Analysis, 19
K. Diethelm, N. Ford (2002)
Analysis of Fractional Differential EquationsJournal of Mathematical Analysis and Applications, 265
S. Hristova (2015)
STABILITY WITH RESPECT TO INITIAL TIME DIFFERENCE FOR GENERALIZED DELAY DIFFERENTIAL EQUATIONS
R. Agarwal, D. O’Regan, S. Hristova, M. Çiçek (2017)
Practical stability with respect to initial time difference for Caputo fractional differential equationsCommun. Nonlinear Sci. Numer. Simul., 42
R. Agarwal, D. O’Regan, S. Hristova (2017)
Stability with Initial Time Difference of Caputo Fractional Differential Equations by Lyapunov FunctionsZeitschrift Fur Analysis Und Ihre Anwendungen, 36
Coșkun Yakar, M. Bayram (2010)
Initial Time Difference Strict Stability Criteria of Fractional Order Differential Equations in Caputo’s Sense ⋆
J. Sabatier, M. Merveillaut, R. Malti, A. Oustaloup (2010)
How to impose physically coherent initial conditions to a fractional systemCommunications in Nonlinear Science and Numerical Simulation, 15
T. Kaczorek, K. Rogowski (2015)
Fractional Differential Equations
Abstract The strict stability properties are generalized to nonlinear Caputo fractional differential equations in the case when both initial points and initial times are changeable. Using Lyapunov functions, some criteria for strict stability, eventually strict stability and strict practical stability are obtained. A brief overview of different types of derivatives in the literature related to the application of Lyapunov functions to Caputo fractional equations are given, and their advantages and disadvantages are discussed with several examples. The Caputo fractional Dini derivative with respect to to initial time difference is used to obtain some sufficient conditions.
Georgian Mathematical Journal – de Gruyter
Published: Mar 1, 2017
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