Journal of Applied Mathematics

Positive Solutions for Multipoint Boundary Value Problems for Singular Fractional Differential Equations

Mohamed Jleli, Erdal Karapinar, and Bessem Samet

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Abstract

A class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 596123, 7 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305585

Digital Object Identifier
doi:10.1155/2014/596123

Mathematical Reviews number (MathSciNet)
MR3178963

Zentralblatt MATH identifier
07010695

Citation

Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem. Positive Solutions for Multipoint Boundary Value Problems for Singular Fractional Differential Equations. J. Appl. Math. 2014 (2014), Article ID 596123, 7 pages. doi:10.1155/2014/596123. https://projecteuclid.org/euclid.jam/1425305585


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References

  • M. Jleli and B. Samet, “On positive solutions for a class of singular nonlinear fractional differential equations,” Boundary Value Problems, vol. 2012, article 73, 2012.
  • 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.
  • G. A. Losa, D. Merlini, T. F. Nonnenmacher, and E. R. Weibel, Eds., Fractals in Biology and Medicine, vol. 2, Birkhäuser, Basel, Switzerland, 1998.
  • S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
  • V. Lakshmikantham, “Theory of fractional functional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 10, pp. 3337–3343, 2008.
  • V. Lakshmikantham and A. S. Vatsala, “Basic theory of fractional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 8, pp. 2677–2682, 2008.
  • V. Lakshmikantham and A. S. Vatsala, “General uniqueness and monotone iterative technique for fractional differential equa-tions,” Applied Mathematics Letters, vol. 21, no. 8, pp. 828–834, 2008.
  • Z. Bai and H. Lü, “Positive solutions for boundary value prob-lem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005.
  • A. M. A. El-Sayed, A. E. M. El-Mesiry, and H. A. A. El-Saka, “On the fractional-order logistic equation,” Applied Mathematics Letters, vol. 20, no. 7, pp. 817–823, 2007.
  • M. El-Shahed, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Abstract and Applied Analysis, vol. 2007, Article ID 10368, 8 pages, 2007.
  • C. Bai, “Positive solutions for nonlinear fractional differential equations with coefficient that changes sign,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 4, pp. 677–685, 2006.
  • C. Bai, “Triple positive solutions for a boundary value problem of nonlinear fractional differential equation,” Electronic Journal of Qualitative Theory of Differential Equations, no. 24, pp. 1–10, 2008.
  • S. Zhang, “Existence of solution for a boundary value problem of fractional order,” Acta Mathematica Scientia B, vol. 26, no. 2, pp. 220–228, 2006.
  • S. Liang and J. Zhang, “Existence and uniqueness of positive solutions to $m$-point boundary value problem for nonlinear fractional differential equation,” Journal of Applied Mathematics and Computing, vol. 38, no. 1-2, pp. 225–241, 2012.
  • X. Xu, D. Jiang, and C. Yuan, “Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 10, pp. 4676–4688, 2009.
  • T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379–1393, 2006.
  • J. Harjani, B. López, and K. Sadarangani, “Fixed point theorems for mixed monotone operators and applications to integral equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 5, pp. 1749–1760, 2011. \endinput