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Stability in delay nonlinear fractional differential equations

Abstract

In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of delay nonlinear fractional differential 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 that \(g\left( t,0\right) =f\left( t,0,0\right) \), which include and improve some related results in the literature.

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Correspondence to Abdelouaheb Ardjouni.

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Boulares, H., Ardjouni, A. & Laskri, Y. Stability in delay nonlinear fractional differential equations. Rend. Circ. Mat. Palermo, II. Ser 65, 243–253 (2016). https://doi.org/10.1007/s12215-016-0230-5

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  • DOI: https://doi.org/10.1007/s12215-016-0230-5

Keywords

  • Delay fractional differential equations
  • Fixed point theory
  • Stability

Mathematics Subject Classification

  • 34K20
  • 34K30
  • 34K40