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Lyapunov stability solutions of fractional integrodifferential equations

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  • Shaher Momani
  • Samir Hadid

Abstract

Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equations x ( α ) ( t ) = f ( t , x ( t ) ) + ∫ t 0 t k ( t , s , x ( s ) ) d s , 0 < α ≤ 1 , with the initial condition x ( α − 1 ) ( t 0 ) = x 0 , have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.

Suggested Citation

  • Shaher Momani & Samir Hadid, 2004. "Lyapunov stability solutions of fractional integrodifferential equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:575670
    DOI: 10.1155/S0161171204312366
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    Cited by:

    1. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2018. "Applications of Lyapunov Functions to Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    2. Hu, D.L. & Chen, W. & Liang, Y.J., 2019. "Inverse Mittag-Leffler stability of structural derivative nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 304-308.
    3. Thabet Abdeljawad & Fadila Madjidi & Fahd Jarad & Ndolane Sene, 2019. "On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
    4. Erman, Sertaç & Demir, Ali, 2020. "On the construction and stability analysis of the solution of linear fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).

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