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Some new Gronwall-type inequalities arising in the research of fractional differential equations. (English) Zbl 1296.26054

Summary: In this paper, some new Gronwall-type inequalities, which can be used as a handy tool in the qualitative and quantitative analysis of the solutions to certain fractional differential equations, are presented. The established results are extensions of some existing Gronwall-type inequalities in the literature. Based on the inequalities established, we investigate the boundedness, uniqueness, and continuous dependence on the initial value and parameter for the solution to a certain fractional differential equation.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26A33 Fractional derivatives and integrals
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