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STABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONS

최성규|강보원|구남집
장전수학회 (Jangjeon Mathematical Society)|2013.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제16권 제2호|pp. 165-174|DOI 10.17777/pjms.2013.16.2.002

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참고문헌

키워드

Caputo fractional differential equationsMittag-Leffler stabilityfractional integral inequalityLyapunov direct method
주제분류수학

초록

This paper deals with the fractional differential equations involvingthe Caputo derivative with order 0 < q < 1. We study boundedness and Mittag-Leffler stability of solutions of Caputo fractional differential equations by usingthe fractional integral inequality and the Lyapunov direct method. Furthermore,we give some examples to illustrate our results.

Abstract

This paper deals with the fractional differential equations involvingthe Caputo derivative with order 0 < q < 1. We study boundedness and Mittag-Leffler stability of solutions of Caputo fractional differential equations by usingthe fractional integral inequality and the Lyapunov direct method. Furthermore,we give some examples to illustrate our results.

참고문헌 (16)

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  10. V. Lakshmikantham, "Theory of Fractional Dynamic Systems" (2009), Cambridge Scientific Publishers Ltd
  11. Y. Li, "Mittag-Leffler stability of fractional order nonlinear dynamic systems", Automatica, 45, pp.1965~1969 (2009)
  12. Y. Li, "Stability of fractioinal-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability", Comput. Math. Appl, 59, pp.1810~1821 (2010)
  13. G. M. Mittag-Leffler, "Sur l’int´egrable de Laplace-Abel", C. R. Acad. Sci. Paris (Ser. II), 136, pp.937~939 (1903)
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