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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.
- R. P. Agarwal, S. Deng, and W. Zhang, “Generalization of a retarded Gronwall-like inequality and its applications,” Applied Mathematics and Computation, vol. 165, no. 3, pp. 599–612, 2005.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2006.
- O. Lipovan, “A retarded Gronwall-like inequality and its applications,” Journal of Mathematical Analysis and Applications, vol. 252, no. 1, pp. 389–401, 2000.
- Q.-H. Ma and J. Pečarić, “Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 894–905, 2008.
- H. Ye and J. Gao, “Henry-Gronwall type retarded integral inequalities and their applications to fractional differential equations with delay,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4152–4160, 2011.
- B. G. Pachpatte, Integral and Finite Difference Inequalities and Applications, Elsevier, Oxford, UK, 2006.
- H. Ye, J. Gao, and Y. Ding, “A generalized Gronwall inequality and its application to a fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 328, no. 2, pp. 1075–1081, 2007.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.