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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 563096, 11 pages
http://dx.doi.org/10.1155/2014/563096
Research Article

Fractional Integral Inequalities via Hadamard’s Fractional Integral

1Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 6 February 2014; Accepted 30 March 2014; Published 22 April 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Weerawat Sudsutad et al. 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.

Linked References

  1. S. Belarbi and Z. Dahmani, “On some new fractional integral inequalities,” Journal of Inequalities in Pure and Applied Mathematics, vol. 10, no. 3, article 86, 5 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Z. Dahmani, “On Minkowski and Hermite-Hadamard integral inequalities via fractional integration,” Annals of Functional Analysis, vol. 1, no. 1, pp. 51–58, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Z. Dahmani, “New inequalities in fractional integrals,” International Journal of Nonlinear Science, vol. 9, no. 4, pp. 493–497, 2010. View at Google Scholar · View at MathSciNet
  4. Z. Dahmani, “The Riemann-Liouville operator to generate some new inequalities,” International Journal of Nonlinear Science, vol. 12, no. 4, pp. 452–455, 2011. View at Google Scholar · View at MathSciNet
  5. Z. Denton and A. S. Vatsala, “Fractional integral inequalities and applications,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1087–1094, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. A. Anastassiou, Fractional Differentiation Inequalities, Springer, New York, NY, USA, 2009. View at MathSciNet
  7. J. Tariboon, S. K. Ntouyas, and W. Sudsutad, “Some new Riemann-Liouville fractional integral inequalities,” International Journal of Mathematics and Mathematical Sciences, vol. 2014, Article ID 869434, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Hadamard, “Essai sur l’etude des fonctions donnees par leur developpment de Taylor,” Journal de Mathématiques Pures et Appliquées, vol. 8, pp. 101–186, 1892. View at Google Scholar
  9. 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. View at MathSciNet
  10. P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, “Compositions of Hadamard-type fractional integration operators and the semigroup property,” Journal of Mathematical Analysis and Applications, vol. 269, no. 2, pp. 387–400, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, “Fractional calculus in the Mellin setting and Hadamard-type fractional integrals,” Journal of Mathematical Analysis and Applications, vol. 269, no. 1, pp. 1–27, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, “Mellin transform analysis and integration by parts for Hadamard-type fractional integrals,” Journal of Mathematical Analysis and Applications, vol. 270, no. 1, pp. 1–15, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. A. A. Kilbas, “Hadamard-type fractional calculus,” Journal of the Korean Mathematical Society, vol. 38, no. 6, pp. 1191–1204, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. A. A. Kilbas and J. J. Trujillo, “Hadamard-type integrals as G-transforms,” Integral Transforms and Special Functions, vol. 14, no. 5, pp. 413–427, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  15. V. L. Chinchane and D. B. Pachpatte, “A note on some integral inequalities via Hadamard integral,” Journal of Fractional Calculus and Applications, vol. 4, pp. 1–5, 2013. View at Google Scholar
  16. V. L. Chinchane and D. B. Pachpatte, “On some integral inequalities using Hadamard fractional integral,” Malaya Journal of Matematik, vol. 1, pp. 62–66, 2012. View at Google Scholar
  17. B. Sroysang, “A study on Hadamard fractional integral,” International Journal of Mathematical Analysis, vol. 7, no. 37–40, pp. 1903–1906, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. F. Jiang and F. Meng, “Explicit bounds on some new nonlinear integral inequalities with delay,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 479–486, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet