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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 217641, 7 pages
Gronwall-Bellman Type Inequalities and Their Applications to Fractional Differential Equations
1School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China
2Department of Mathematics, Jining University, Qufu, Shandong 273155, China
Received 29 May 2013; Accepted 22 July 2013
Academic Editor: Irena Lasiecka
Copyright © 2013 Jing Shao and Fanwei Meng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [11 citations]
The following is the list of published articles that have cited the current article.
- Phollakrit Thiramanus, Jessada Tariboon, and Sotiris K. Ntouyas, “Integral inequalities with 'maxima' and their applications to Hadamard type fractional differential equations,” Journal Of Inequalities And Applications, 2014.
- Phollakrit Thiramanus, Jessada Tariboon, and Sotiris K. Ntouyas, “Henry-Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014.
- Jing Shao, “New Integral Inequalities with Weakly Singular Kernel for Discontinuous Functions and Their Applications to Impulsive Fractional Differential Systems,” Journal of Applied Mathematics, vol. 2014, pp. 1–5, 2014.
- Shi-you Lin, “New Results for Generalized Gronwall Inequalities and Their Applications,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014.
- Xiaoling Fu, Huixuan Wang, Naxin Cui, and Chenghui Zhang, “Energy Management Strategy Based on the Driving Cycle Model for Plugin Hybrid Electric Vehicles,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 2014.
- Kelong Cheng, Chunxiang Guo, and Min Tang, “Some Nonlinear Gronwall-Bellman-Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014.
- Bin Zheng, “Some New Discrete Fractional Inequalities And Their Applications In Fractional Difference Equations,” Journal Of Mathematical Inequalities, vol. 9, no. 3, pp. 823–839, 2015.
- Haidong Liu, and Fanwei Meng, “Some new nonlinear integral inequalities with weakly singular kernel and their applications to FDEs,” Journal Of Inequalities And Applications, 2015.
- Qinghua Feng, “Some new generalized Gronwall-Bellman type discrete fractional inequalities,” Applied Mathematics And Computation, vol. 259, pp. 403–411, 2015.
- Run Xu, and Fanwei Meng, “Some new weakly singular integral inequalities and their applications to fractional differential equations,” Journal Of Inequalities And Applications, 2016.
- Yuehjen E. Shao, “Using a Computational Intelligence Hybrid Approach to Recognize the Faults of Variance Shifts for a Manufacturing Process,” Journal of Industrial and Intelligent Information, 2016.