Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

POSITIVE SOLUTIONS FOR MULTI-POINT BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Wang, Haihua (Department of Mathematics, Hunan University of Science and Technology)
  • 투고 : 2010.11.24
  • 심사 : 2011.06.08
  • 발행 : 2012.01.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we establish some sufficient conditions for the existence of positive solutions for a class of multi-point boundary value problem for fractional functional differential equations involving the Caputo fractional derivative. Our results are based on two fixed point theorems. Two examples are also provided to illustrate our main results.

키워드

참고문헌

  1. R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta. Appl. Math. 109 (2010), 973-1033. https://doi.org/10.1007/s10440-008-9356-6
  2. C. Bai, Triple positive solutions for a boundary value problem of nonlinear fractional differential equation, Electron. J. Qual. Theory Differ. Equ. 24 (2008), 1-10.
  3. Z. Bai, H. Lu, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005), 495-505. https://doi.org/10.1016/j.jmaa.2005.02.052
  4. D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press Inc., New Yok, 1988.
  5. E.R. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electron. J. Qual. Theory Differ. Equ. 3 (2008), 1-11.
  6. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier, Amsterdam, 2006.
  7. R.W. Leggett, L.R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach space, Indiana Univ. Math. J. 28 (1979), 673-688. https://doi.org/10.1512/iumj.1979.28.28046
  8. C. Li, X. Luo, Y. Zhou, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Comput. Math. Appl. 59 (2010), 1363-1375. https://doi.org/10.1016/j.camwa.2009.06.029
  9. S. Zhang, Positive solutions to singular boundary value problem for nonlinear fractional differential equation, Comput. Math. Appl. 59 (2010), 1300-1309. https://doi.org/10.1016/j.camwa.2009.06.034
  10. S. Zhang, Existence of positive solution for some class of nonlinear fractional differential equations, J. Math. Anal. Appl. 278 (2003), 136-148. https://doi.org/10.1016/S0022-247X(02)00583-8
  11. S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differ. Equ. 36 (2006), 1-12.