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Some new generalized Gronwall–Bellman type discrete fractional inequalities

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  • Feng, Qinghua

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.

Suggested Citation

  • Feng, Qinghua, 2015. "Some new generalized Gronwall–Bellman type discrete fractional inequalities," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 403-411.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:403-411
    DOI: 10.1016/j.amc.2015.03.012
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    Cited by:

    1. Ma, Wangrong & Jin, Maozhu & Liu, Yifeng & Xu, Xiaobo, 2019. "Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 17-23.

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