DOI QR코드

DOI QR Code

A QUADRATIC INTEGRAL EQUATION IN THE SPACE OF FUNCTIONS WITH TEMPERED MODULI OF CONTINUITY

PENG, SHAN;WANG, JINRONG;CHEN, FULAI

  • 투고 : 2014.07.25
  • 심사 : 2014.11.04
  • 발행 : 2015.05.30

초록

In this paper, we investigate existence of solutions to a class of quadratic integral equation of Fredholm type in the space of functions with tempered moduli of continuity. Two numerical examples are given to illustrate our results.

키워드

Quadratic integral equation;Tempered moduli of continuity;Schauder fixed point theorem

참고문헌

  1. M.A, Darwish and S.K. Ntouyas, On a quadratic fractional Hammerstein-Volterra integral equations with linear modification of the argument, Nonlinear Anal., 74(2011), 3510-3517. https://doi.org/10.1016/j.na.2011.02.035
  2. M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl., 311(2005), 112-119. https://doi.org/10.1016/j.jmaa.2005.02.012
  3. R.P. Agarwal, J. Banaś, K. Banaś and D. O’Regan, Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity, J. Int. Eq. Appl., 23(2011), 157-181. https://doi.org/10.1216/JIE-2011-23-2-157
  4. J. Wang, X. Dong and Y. Zhou, Existence, attractiveness and stability of solutions for quadratic Urysohn fractional integral equations, Commun. Nonlinear Sci. Numer. Simul., 17(2012), 545-554. https://doi.org/10.1016/j.cnsns.2011.05.034
  5. J. Wang, X. Dong and Y. Zhou, Analysis of nonlinear integral equations with Erd´elyi-Kober fractional operator, Commun. Nonlinear Sci. Numer. Simul., 17(2012), 3129-3139. https://doi.org/10.1016/j.cnsns.2011.12.002
  6. J. Wang, C. Zhu and Y. Zhou, Study on a quadratic Hadamard types fractional integral equation on an unbounded interval, Topological Methods in Nonlinear Analysis, 42(2013), 257-275.
  7. J. Banaś and R. Nalepa, On the space of functions with growths tempered by a modulus of continuity and its applications, Journal of Function Spaces and Applications, 2013(2013), Article ID 820437, 13 pages.
  8. J. Caballero, M.A. Darwish and K. Sadarangani, Solvability of a quadratic integral equation of Fredholm type in Hölder spaces, Electronic Journal of Differential Equations, 2014(2014), No.31, 1-10.
  9. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  10. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  11. V.E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, HEP, 2010.
  12. K.M. Case, P.F. Zweifel, Linear Transport Theory, Addison Wesley, Reading, M. A, 1967.
  13. S. Chandrasekhar, Radiative transfer, Dover Publications, New York, 1960.
  14. S. Hu, M. Khavani, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal., 34(1989), 261-266. https://doi.org/10.1080/00036818908839899
  15. C.T. Kelly, Approximation of solutions of some quadratic integral equations in transport theory, J. Int. Eq., 4(1982), 221-237.
  16. J. Banaś, M. Lecko and W.G. El-Sayed, Existence theorems of some quadratic integral equation, J. Math. Anal. Appl., 222(1998), 276-285. https://doi.org/10.1006/jmaa.1998.5941
  17. J. Banaś, J. Caballero, J. Rocha and K. Sadarangani, Monotonic solutions of a class of quadratic integral equations of Volterra type, Comput. Math. Appl., 49(2005), 943-952. https://doi.org/10.1016/j.camwa.2003.11.001
  18. J. Caballero, J. Rocha and K. Sadarangani, On monotonic solutions of an integral equation of Volterra type, J. Comput. Appl. Math., 174(2005), 119-133. https://doi.org/10.1016/j.cam.2004.04.003
  19. M.A. Darwish, On solvability of some quadratic functional-integral equation in Banach algebras, Commun. Appl. Anal., 11(2007), 441-450.
  20. D. Baleanu, J.A.T. Machado and A.C.-J. Luo, Fractional Dynamics and Control, Springer, 2012.
  21. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of frac- tional differential equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B. V., Amsterdam, 2006.
  22. V. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, 2009.