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

By Nguyen Dinh Cong, Hoang The Tuan. 2017

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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.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

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