Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 184626, 7 pages
http://dx.doi.org/10.1155/2014/184626
Research Article

On Solutions of a Nonlinear Erdélyi-Kober Integral Equation

1Department of Mathematics, Science-Pedagogical Faculty, M. Auezov South Kazakhstan State University, Tauke Khan Avenue 5, Shymkent 160012, Kazakhstan
2Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland

Received 27 April 2014; Accepted 18 May 2014; Published 1 June 2014

Academic Editor: Robert A. Van Gorder

Copyright © 2014 Nurgali K. Ashirbayev 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. K. Diethelm, The Analysis of Fractional Differential Equations, vol. 2004 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier Science B.V., Amsterdam, The Netherlands, 2006. View at MathSciNet
  3. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  4. I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  5. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  6. V. Lakshmikantham, S. Leela, and J. Vasundara Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, Cambridge, UK, 2009.
  7. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Amsterdam, The Netherlands, 1993. View at MathSciNet
  8. H. M. Srivastava and R. K. Saxena, “Operators of fractional integration and their applications,” Applied Mathematics and Computation, vol. 118, no. 1, pp. 1–52, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. A. Alamo and J. Rodríguez, “Operational calculus for modified Erdélyi-Kober operators,” Serdica Bulgaricae Mathematicae Publicationes, vol. 20, no. 3-4, pp. 351–363, 1994. View at Google Scholar · View at MathSciNet
  10. H. H. Hashem and M. S. Zaki, “Carathéodory theorem for quadratic integral equations of Erdélyi-Kober type,” Journal of Fractional Calculus and Applications, vol. 4, no. 1, pp. 56–72, 2013. View at Google Scholar
  11. M. A. Darwish and K. Sadarangani, “On Erdélyi-Kober type quadratic integral equation with linear modification of the argument,” Applied Mathematisc and Computation, vol. 238, pp. 30–42, 2014. View at Google Scholar
  12. J. R. Wang, C. Zhu, and M. Feckan, “Solvability of fully nonlinear functional equations involving Erdélyi-Kober fractional integrals on the unbounded interval,” Optimization, 2014. View at Publisher · View at Google Scholar
  13. J. Appell, J. Banaś, and N. Merentes, Bounded Variation and Around, vol. 17 of De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, Germany, 2014. View at MathSciNet
  14. I. P. Natanson, Theory of Functions of a Real Variable, Ungar, New York, NY, USA, 1960.
  15. N. Danford and J. T. Schwartz, Linear Operators, International Publishing, Leyden, The Netherlands, 1963.
  16. A. Erdélyi, “On fractional integration and its application to the theory of Hankel transforms,” The Quarterly Journal of Mathematics, vol. 11, p. 293–-303, 1940. View at Google Scholar · View at MathSciNet
  17. A. Erdélyi and H. Kober, “Some remarks on Hankel transforms,” The Quarterly Journal of Mathematics, vol. 11, pp. 212–221, 1940. View at Google Scholar · View at MathSciNet
  18. H. Kober, “On fractional integrals and derivatives,” The Quarterly Journal of Mathematics, vol. 11, pp. 193–211, 1940. View at Google Scholar · View at MathSciNet
  19. J. Banaś and T. Zając, “A new approach to the theory of functional integral equations of fractional order,” Journal of Mathematical Analysis and Applications, vol. 375, no. 2, pp. 375–387, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  20. T. Zając, “Solvability of fractional integral equations on an unbounded interval through the theory of Volterra-Stieltjes integral equations,” Zeitschrift für Analysis und ihre Anwendungen, vol. 33, no. 1, pp. 65–85, 2014. View at Publisher · View at Google Scholar · View at MathSciNet