Some new generalized Gronwall–Bellman type discrete fractional inequalities

Qinghua Feng

Applied Mathematics and Computation, 2015, vol. 259, issue C, 403-411

Abstract: In this paper, we present some new generalized Gronwall–Bellman type discrete fractional inequalities including fractional sum inequalities and fractional difference inequalities. These inequalities are of new forms compared with the existing results so far in the literature, and can be used to provide explicit bounds for unknown functions concerned. For illustrating the effectiveness of the presented results, we apply them to research qualitative and quantitative properties for the solutions of an IVP with respect to a fractional difference equation.

Keywords: Gronwall–Bellman type inequality; Discrete fractional difference inequality; Fractional sum inequality; Fractional difference equation; Boundedness (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:403-411

DOI: 10.1016/j.amc.2015.03.012

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