Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2018, Article ID 2352789, 8 pages
https://doi.org/10.1155/2018/2352789
Research Article

Existence Results for Fractional Differential Equations with Multistrip Riemann–Stieltjes Integral Boundary Conditions

1College of Science, China Agricultural University, Beijing 100083, China
2School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Correspondence should be addressed to Huihui Pang; moc.361@0002hhp

Received 29 December 2017; Revised 28 February 2018; Accepted 20 March 2018; Published 24 April 2018

Academic Editor: Chris Goodrich

Copyright © 2018 Tongling Lv 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. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999. View at MathSciNet
  2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, Elsevier, 2006. View at MathSciNet
  3. V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, Cambridge, 2009.
  4. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  5. Z. Bai, “On positive solutions of a nonlocal fractional boundary value problem,” Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal, vol. 72, no. 2, pp. 916–924, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. Jiang and C. Yuan, “The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 2, pp. 710–719, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  7. T. Jankowski, “Boundary problems for fractional differential equations,” Applied Mathematics Letters, vol. 28, pp. 14–19, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. L. Lin, X. Liu, and H. Fang, “Method of upper and lower solutions for fractional differential equations,” Electronic Journal of Differential Equations, vol. 2012, 2012. View at Google Scholar · View at MathSciNet
  9. Z. B. Bai, S. Zhang, S. J. Sun, and C. Yin, “Monotone iterative method for a class of fractional differential equations,” Electronic Journal of Differential Equations, vol. No. 06, p. 2016, 2016. View at Google Scholar
  10. X. Zhang and Q. Zhong, “Multiple positive solutions for nonlocal boundary value problems of singular fractional differential equations,” Boundary Value Problems, Paper No. 65, 11 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. W. Yang, “Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 288–297, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. R. A. Khan, M. ur Rehman, and J. Henderson, “Existence and uniqueness of solutions for nonlinear fractional differential equations with integral boundary conditions,” Fractional Differential Calculus, vol. 1, no. 1, pp. 29–43, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Jin, X. Liu, and M. Jia, “Existence of positive solutions for singular fractional differential equations with integral boundary conditions,” Electronic Journal of Differential Equations, No. 63, 14 pages, 2012. View at Google Scholar · View at MathSciNet
  14. M. Feng, X. Zhang, and W. Ge, “New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions,” Boundary Value Problems, vol. 2011, Article ID 720702, 20 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. D. Min, L. Liu, and Y. Wu, “Uniqueness of positive solutions for the singular fractional differential equations involving integral boundary value conditions,” Boundary Value Problems, 2018:23 pages, 2018. View at Publisher · View at Google Scholar · View at MathSciNet
  16. X. Liu, L. Liu, and Y. Wu, “Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives,” Boundary Value Problems, 2018:24 pages, 2018. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. Sun and M. Zhao, “Positive solutions for a class of fractional differential equations with integral boundary conditions,” Applied Mathematics Letters, vol. 34, pp. 17–21, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. H.-E. Zhang, “Iterative solutions for fractional nonlocal boundary value problems involving integral conditions,” Boundary Value Problems, Paper No. 3, 13 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus