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Gronwall-Bellman type inequalities and their applications to fractional differential equations. (English) Zbl 1297.34010

Summary: Some new weakly singular integral inequalities of Gronwall-Bellman type are established, which can be used in the qualitative analysis of the solutions to certain fractional differential equations.

MSC:

34A08 Fractional ordinary differential equations
26D10 Inequalities involving derivatives and differential and integral operators
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References:

[1] Agarwal, R. P.; Deng, S.; Zhang, W., Generalization of a retarded Gronwall-like inequality and its applications, Applied Mathematics and Computation, 165, 3, 599-612 (2005) · Zbl 1078.26010 · doi:10.1016/j.amc.2004.04.067
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[6] Pachpatte, B. G., Integral and Finite Difference Inequalities and Applications (2006), Oxford, UK: Elsevier, Oxford, UK · Zbl 1104.26015 · doi:10.1016/S0304-0208(06)80012-5
[7] Ye, H.; Gao, J.; Ding, Y., A generalized Gronwall inequality and its application to a fractional differential equation, Journal of Mathematical Analysis and Applications, 328, 2, 1075-1081 (2007) · Zbl 1120.26003 · doi:10.1016/j.jmaa.2006.05.061
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