Lyapunov Characterization of the Fractional Nonlinear Systems with Exogenous Input

Sene, Ndolane

doi:10.3390/fractalfract2020017

Cited by 18 publications

(16 citation statements)

References 26 publications

(34 reference statements)

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“…The issue is to study the stability and convergence. The stability analysis of the fractional differential equations has received many investigations in literature [8,9,11,13,18]. For recent investigations in stability analysis, see the following papers [3,18].…”

Section: Introductionmentioning

confidence: 99%

Global asymptotic stability of the fractional differential equations

Sene¹

2019

J. Nonlinear Sci. Appl.

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In this note, we present a global asymptotic stability criterion for the fractional differential equations in triangular form. We use the Caputo generalized fractional derivative in our investigations. In our note, we introduce a new procedure to study the global asymptotic stability of the fractional differential equations.Keywords: Caputo left generalized fractional derivative, fractional differential equations with input, Mittag-Leffler input stability.2010 MSC: 93D25, 93D05, 26A33.

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Section: Introductionmentioning

confidence: 99%

Global asymptotic stability of the fractional differential equations

Sene¹

2019

J. Nonlinear Sci. Appl.

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“…From assumption |arg(λ(A))| > απ 2 , there exist a positive number M > 0 [4,18,34] such that, we have…”

Section: New Stability Notion Of the Fractional Differential Equationsmentioning

confidence: 99%

“…Let us consider k = σ 1−α R L − 1 2 and θ ∈ (0, 1). We have the following relationship Let us consider the fractional differential equation described in [4] by the left generalized fractional differential equation defined by D α,ρ…”

Section: Practical Applicationsmentioning

confidence: 99%

“…In [3], Souahi et al propose some new Lyapunov characterizations of fractional differential equations described by the conformable fractional derivative. In [4], Sene proposes a new stability notion and introduce the Lyapunov characterization of the conditional asymptotic stability. In [5,6], Sene proposes some applications of the fractional input stability to the electrical circuits described the Liouville-Caputo fractional derivative and the Riemann-Liouville fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations

Sene

Srivastava

2019

Symmetry

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The behavior of the analytical solutions of the fractional differential equation described by the fractional order derivative operators is the main subject in many stability problems. In this paper, we present a new stability notion of the fractional differential equations with exogenous input. Motivated by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, we present our work here. Applications of Mittag-Leffler functions in certain areas of physical and applied sciences are also very common. During the last two decades, this class of functions has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittag-Leffler, due to the vast potential of its applications in solving the problems of physical, biological, engineering, and earth sciences, to name just a few. Moreover, we propose the generalized Mittag-Leffler input stability conditions. The left generalized fractional differential equation has been used to help create this new notion. We investigate in depth here the Lyapunov characterizations of the generalized Mittag-Leffler input stability of the fractional differential equation with input.

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“…In the rest of this paper, we use the Caputo idea of the fractional derivative. There exists many investigations related to the stability analysis of the FDEs in the literature: in [18] some conditions for the stability notions of the fractional differential equations using the Riemann-Liouville derivative were proposed, in [20] some conditions for the stability for a particular class of conformable differential equations were also proposed, in [19] some conditions for stability respect to small inputs were proposed to study the behavior of the solutions of the fractional differential equations with exogenous inputs, etc.…”

Section: Introductionmentioning

confidence: 99%

Exponential form for Lyapunov function and stability analysis of the fractional differential equations

Sene¹

2018

J. Math. Computer Sci.

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This paper deals with an exponential form for Lyapunov function, in perspective to analyze the Lyapunov characterization of the Mittag-Leffler stability and the asymptotic stability for the fractional differential equations. In addition, a new Lyapunov characterization of Mittag-Leffler stability for fractional differential equations will be introduced. The exponential form will be used to prove the Lyapunov characterization of several stability notions, used in fractional differential equations. In this paper, the Caputo fractional derivative operator will be used to do the studies.

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Lyapunov Characterization of the Fractional Nonlinear Systems with Exogenous Input

Cited by 18 publications

References 26 publications

Global asymptotic stability of the fractional differential equations

Global asymptotic stability of the fractional differential equations

Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations

Exponential form for Lyapunov function and stability analysis of the fractional differential equations

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