International Journal of Differential Equations

Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations

Jinhua Wang, Hongjun Xiang, and Zhigang Liu

Full-text: Open access

Abstract

We consider the existence and uniqueness of positive solution to nonzero boundary values problem for a coupled system of fractional differential equations. The differential operator is taken in the standard Riemann-Liouville sense. By using Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, the existence and uniqueness of positive solution are obtained. Two examples are given to demonstrate the feasibility of the obtained results.

Article information

Source
Int. J. Differ. Equ., Volume 2010, Special Issue (2010), Article ID 186928, 12 pages.

Dates
Received: 13 April 2009
Accepted: 9 June 2009
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399873

Digital Object Identifier
doi:10.1155/2010/186928

Mathematical Reviews number (MathSciNet)
MR2525726

Zentralblatt MATH identifier
1207.34012

Citation

Wang, Jinhua; Xiang, Hongjun; Liu, Zhigang. Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations. Int. J. Differ. Equ. 2010, Special Issue (2010), Article ID 186928, 12 pages. doi:10.1155/2010/186928. https://projecteuclid.org/euclid.ijde/1485399873


Export citation

References

  • C. Bai and J. Fang, “The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 611–621, 2004.MR2039662
  • X. Su, “Boundary value problem for a coupled system of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 22, no. 1, pp. 64–69, 2009.MR2483163
  • Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005.MR2168413
  • S. Zhang, “Existence of solution for a boundary value problem of fractional order,” Acta Mathematica Scientia, vol. 26, no. 2, pp. 220–228, 2006.
  • S. Q. Zhang, “Positive of solution for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, vol. 36, pp. 1–12, 2006.
  • I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.MR1658022
  • 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 Science, Amsterdam, The Netherlands, 2006.MR2218073
  • E. Zeidler, Nonlinear Functional Analysis and Its Applications–-I: Fixed-Point Theorems, Springer, New York, NY, USA, 1986.MR816732