Existence, Uniqueness, and Exponential Boundedness of Global Solutions to Delay Fractional Differential Equations

Abstract

In this paper, using properties of Mittag–Leffler functions, a weighted norm, and the Banach fixed point theorem, we establish a rigorous theorem on the existence and uniqueness of global solutions to delay fractional differential equations under a mild Lipschitz condition. Then, we provide a sufficient condition which guarantees these solutions to be exponentially bounded. Our theorems fill the gaps and also strengthen results in some existing papers.

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Correspondence to H. T. Tuan.

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Cong, N.D., Tuan, H.T. Existence, Uniqueness, and Exponential Boundedness of Global Solutions to Delay Fractional Differential Equations. Mediterr. J. Math. 14, 193 (2017). https://doi.org/10.1007/s00009-017-0997-4

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Mathematics Subject Classification

  • 26A33
  • 34A08
  • 34A12
  • 34K12

Keywords

  • Fractional differential equations
  • delay differential equations with fractional derivatives
  • existence and uniqueness
  • growth and boundedness