Geodesic
Global asymptotic stability of the fractional differential equations
Sene, Ndolane 1
1 Laboratoire Lmdan, Departement de Mathematiques de la Decision, Universite Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal
Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 3, p. 171-175.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.013.03.06
Classification : 93D25, 93D05, 26A33
Keywords: Caputo left generalized fractional derivative, fractional differential equations with input, Mittag-Leffler input stability

Sene, Ndolane  1

1 Laboratoire Lmdan, Departement de Mathematiques de la Decision, Universite Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal 
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Sene, Ndolane . Global asymptotic stability of the fractional differential equations. Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 3, p. 171-175. doi : 10.22436/jnsa.013.03.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.03.06/

[1] Abdeljawad, T.; Madjidi, F.; Jarad, F.; Sene, N. On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives, Mathematics, Volume 7 (2019), pp. 1-13 | DOI

[2] Adjabi, Y.; Jarad, F.; Abdeljawad, T. On generalized fractional operators and a Gronwall type inequality with applications, Filomat, Volume 31 (2017), pp. 5457-5473 | Zbl | DOI

[3] Makhlouf, A. Ben Stability with respect to part of the variables of nonlinear Caputo fractional differential equations, Math. Commun., Volume 23 (2018), pp. 119-126 | Zbl

[4] Gambo, Y. Y.; Ameen, R.; Jarad, F.; Abdeljawad, T. Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives, Adv. Difference Equ., Volume 2018 (2018), pp. 1-13 | DOI | Zbl

[5] Jarad, F.; Abdeljawad, T. A modified laplace transform for certain generalized fractional operators, Results Nonlinear Anal., Volume 2 (2018), pp. 88-98

[6] Jarad, F.; Uğurlu, E.; Abdeljawad, T.; Baleanu, D. On a new class of fractional operators, Adv. Difference Equ., Volume 1 (2017), pp. 1-16 | DOI | Zbl

[7] Katugampola, U. N. New approach to a generalized fractional integral, Appl. Math. Comput., Volume 218 (2011), pp. 860-865 | Zbl | DOI

[8] Sene, N. Exponential form for lyapunov function and stability analysis of the fractional differential equations, J. Math. Computer Sci., Volume 18 (2018), pp. 388-397

[9] Sene, N. Lyapunov characterization of the fractional nonlinear systems with exogenous input, Fractal Fract., Volume 2 (2018), pp. 1-10 | DOI

[10] Sene, N. Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives, AIMS Math., Volume 4 (2019), pp. 147-165

[11] Sene, N. Fractional input stability and its application to neural network, Discrete Contin. Dyn. Syst. Ser. S, Volume 13 (2019), pp. 853-865

[12] Sene, N. Mittag-Leffler input stability of fractional differential equations and its applications, Discrete Contin. Dyn. Syst. Ser. S, Volume 13 (2019), pp. 867-880 | DOI

[13] Sene, N. Stability analysis of the generalized fractional differential equations with and without exogenous inputs, J. Nonlinear Sci. Appl., Volume 12 (2019), pp. 562-572

[14] Sene, N. Solution of fractional diffusion equations and Cattaneo-Hristov diffusion model, Int. J. Anal. Appl., Volume 17 (2019), pp. 191-207

[15] Sene, N.; Chaillet, A.; Balde, M. Relaxed conditions for the stability of switched nonlinear triangular systems under arbitrary switching, Systems Control Lett., Volume 84 (2015), pp. 52-56 | DOI | Zbl

[16] Sene, N.; Fall, A. N. Homotopy Perturbation $\rho$-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation, Fract. Frac., Volume 3 (2019), pp. 1-15 | DOI

[17] Sene, N.; Srivastava, G. Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations, Symmetry, Volume 11 (2019), pp. 1-12 | Zbl | DOI

[18] Souahi, A.; Makhlouf, A. Ben; Hammami, M. A. Stability analysis of conformable fractional-order nonlinear systems, Indag. Math. (N.S.), Volume 28 (2017), pp. 1265-1274 | DOI | Zbl

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