Global asymptotic stability of the fractional differential equations

Sene, Ndolane

doi:10.22436/jnsa.013.03.06

Cited by 21 publications

(35 citation statements)

References 14 publications

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“…Using the fixed point technique (Alternative theorem), we study HUR stability of the φ-Hadamard fractional Volterra integro-differential equation (23) in MVFB-space (W, S , ). Our results can apply to improve recent results [17] and by methods used in this paper we can extend some fractional Volterra integro-differential equations in MVFBspaces [18][19][20].…”

Section: φ-Hadamard Fractional Equationssupporting

confidence: 61%

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Aderyani

Saadati

2021

Adv Differ Equ

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In this article, first, we present an example of fuzzy normed space by means of the Mittag-Leffler function. Next, we extend the concept of fuzzy normed space to matrix valued fuzzy normed space and also we introduce a class of matrix valued fuzzy control functions to stabilize a nonlinear ϕ-Hadamard fractional Volterra integro-differential equation. In this sense, we investigate the Ulam–Hyers–Rassias stability for this kind of fractional equations in matrix valued fuzzy Banach space. Finally, as an application, we investigate the Ulam–Hyers–Rassias stability using matrix valued fuzzy control function obtained through the Mittag-Leffler function.

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Section: φ-Hadamard Fractional Equationssupporting

confidence: 61%

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Aderyani

Saadati

2021

Adv Differ Equ

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“…showing the boundedness of π. Now, we show that π satisfies (27). Let t = s = 0, then (27) is trivial.…”

Section: Corollary 16mentioning

confidence: 92%

“…Recently, the stability problems of several functional equations (FEs) have been extensively investigated by a number of authors [4,[9][10][11][12][13][14][15][16][17][18][19][20] in Felbin type f-NLS. Our method helps to solve some new problems of stability and approximation of functional equations [21][22][23][24][25][26][27][28] in Felbin type f-NLS.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Mixed Euler-Lagrange $σ$ -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS

Rassias

Narasimman

Saadati

et al. 2021

Journal of Function Spaces

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In this research paper, the authors present a new mixed Euler-Lagrange σ -cubic-quartic functional equation. For this introduced mixed type functional equation, the authors obtain general solution and investigate the various stabilities related to the Ulam problem in Felbin’s type of fuzzy normed linear space (f-NLS) with suitable counterexamples. This approach leads us to approximate the Euler-Lagrange σ -cubic-quartic functional equation with better estimation.

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“…Recent years fractional calculus [17,28] have emerged and attracted many authors. This new field finds much application in the following areas: physics [11,16,29,31], mechanics, biology [30], mathematical physics [16,19,22], electrical circuits [20], economics, modeling fluids [21,25] and many others [12,24,27]. Following this direction, the Chua's system is remodeled in this paper using the Caputo-Liouville fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

Sene¹

2021

Rev. Mex. Fís.

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This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

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Global asymptotic stability of the fractional differential equations

Cited by 21 publications

References 14 publications

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Approximation of Mixed Euler-Lagrange $σ$ -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

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Global asymptotic stability of the fractional differential equations

Cited by 21 publications

References 14 publications

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Approximation of Mixed Euler-Lagrange σ -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

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Approximation of Mixed Euler-Lagrange $σ$ -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS