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Gronwall-Bellman Type Inequalities and Their Applications to Fractional Differential Equations

Author

Listed:
  • Jing Shao
  • Fanwei Meng

Abstract

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.

Suggested Citation

  • Jing Shao & Fanwei Meng, 2013. "Gronwall-Bellman Type Inequalities and Their Applications to Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, August.
    • Handle: RePEc:hin:jnlaaa:217641
    DOI: 10.1155/2013/217641
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    Cited by:

    1. Jing Shao, 2014. "New Integral Inequalities with Weakly Singular Kernel for Discontinuous Functions and Their Applications to Impulsive Fractional Differential Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Phollakrit Thiramanus & Jessada Tariboon & Sotiris K. Ntouyas, 2014. "Henry‐Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Kelong Cheng & Chunxiang Guo & Min Tang, 2014. "Some Nonlinear Gronwall‐Bellman‐Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Xiaoling Fu & Huixuan Wang & Naxin Cui & Chenghui Zhang, 2014. "Energy Management Strategy Based on the Driving Cycle Model for Plugin Hybrid Electric Vehicles," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Omaba, McSylvester Ejighikeme, 2021. "Growth moment, stability and asymptotic behaviours of solution to a class of time-fractal-fractional stochastic differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. Shi-you Lin, 2014. "New Results for Generalized Gronwall Inequalities and Their Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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