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

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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.

Keywords

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

Mathematics Subject Classification

26A33 34A08 34A12 34K12 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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