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.
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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