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STABILITY BY KRASNOSELSKII'S FIXED POINT THEOREM FOR NONLINEAR FRACTIONAL DYNAMIC EQUATIONS ON A TIME SCALE

Belaid, Malik;Ardjouni, Abdelouaheb;Boulares, Hamid;Djoudi, Ahcene

  • Received : 2017.12.30
  • Accepted : 2019.01.14
  • Published : 2019.03.25

Abstract

In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of nonlinear fractional dynamic equations of order ${\alpha}$ (1 < ${\alpha}$ < 2). By using the Krasnoselskii's fixed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided f (t, 0) = 0, which include and improve some related results in the literature.

Keywords

Fixed points;fractional dynamic equations;asymptotic stability;time scales