Research Article
BibTex RIS Cite

The multiplicity of positive solutions for systems of fractional boundary value problems

Year 2019, Volume: 48 Issue: 6 , 1626 - 1634 , 08.12.2019
https://izlik.org/JA27XF75NH

Abstract

This paper focuses on the multiple positive solutions for a coupled system of nonlinear boundary value problems of fractional order. Our approach is based on a fixed point theorem due to Bai and Ge. Also, an example is given to demonstrate the applicability of our main result.

References

  • [1] Z.E. Abidine, Multiple Positive Solutions for a Coupled System of Nonlinear Fractional Differential Equations on the Half-line, Mediterr. J. Math. 14, Article No: 142, 16 pages, 2017.
  • [2] B. Ahmad and J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58, 1838-1843, 2009.
  • [3] B. Ahmad, J.J. Nieto, A. Alsaedi and M.H. Aqlan, A Coupled System of Caputo-Type Sequential Fractional Differential Equations with Coupled (Periodic/Anti-periodic Type) Boundary Conditions, Mediterr. J. Math. 14, Article No: 227, 2017.
  • [4] Z. Bai and W. Ge, Existence of three positive solutions for some second-order boundary value problems, Comput. Math. Appl. 48, 699-707, 2004.
  • [5] T.S. Cerdik, N.A. Hamal and F. Yoruk Deren, Existence of solutions for nonlinear fractional differential equations with m-point integral boundary conditions, Dynam. Systems Appl. 24, 283-294, 2015.
  • [6] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
  • [7] J. Henderson and R. Luca, Positive solutions for a system of nonlocal fractional boundary value problems, Fract. Calc. Appl. Anal. 16 (4), 985-1008, 2013.
  • [8] J. Henderson and R. Luca, Positive solutions for a system of semipositone coupled fractional boundary value problems, Bound. Value Probl. 2016, Article No: 61, 2016.
  • [9] J. Henderson and R. Luca, Systems of Riemann-Liouville fractional equations with multi-point boundary conditions, Appl. Math. Comput. 309, 303-323, 2017.
  • [10] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, in: North-Holland Mathematics Studies 204, Elsevier Science B.V, Amsterdam, 2006.
  • [11] Y. Liu, New existence results for positive solutions of boundary value problems for coupled systems of multi-term fractional differential equations, Hacet. J. Math. Stat. 45 (2), 391-416, 2016.
  • [12] N. Nyamoradi, Multiple positive solutions for fractional differential systems, Ann Univ Ferrara 58, 359-369, 2012.
  • [13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [14] X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett. 22, 64-69, 2009.
  • [15] Y.Wang, Positive solutions for a system of fractional integral boundary value problem, Bound. Value Probl. 2013, Article No: 256, 2013.
  • [16] A. Yang and W. Ge, Positive Solutions for Boundary Value Problems of N-Dimension Nonlinear Fractional Differential System, Bound. Value Probl. 2008, Article ID 437453, 15 pages, 2008.
  • [17] A. Yang and H. Wang, Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition, Electron. J. Qual. Theory Differ. Equ. 2011 (1), 1-15, 2011.

Year 2019, Volume: 48 Issue: 6 , 1626 - 1634 , 08.12.2019
https://izlik.org/JA27XF75NH

Abstract

References

  • [1] Z.E. Abidine, Multiple Positive Solutions for a Coupled System of Nonlinear Fractional Differential Equations on the Half-line, Mediterr. J. Math. 14, Article No: 142, 16 pages, 2017.
  • [2] B. Ahmad and J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58, 1838-1843, 2009.
  • [3] B. Ahmad, J.J. Nieto, A. Alsaedi and M.H. Aqlan, A Coupled System of Caputo-Type Sequential Fractional Differential Equations with Coupled (Periodic/Anti-periodic Type) Boundary Conditions, Mediterr. J. Math. 14, Article No: 227, 2017.
  • [4] Z. Bai and W. Ge, Existence of three positive solutions for some second-order boundary value problems, Comput. Math. Appl. 48, 699-707, 2004.
  • [5] T.S. Cerdik, N.A. Hamal and F. Yoruk Deren, Existence of solutions for nonlinear fractional differential equations with m-point integral boundary conditions, Dynam. Systems Appl. 24, 283-294, 2015.
  • [6] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
  • [7] J. Henderson and R. Luca, Positive solutions for a system of nonlocal fractional boundary value problems, Fract. Calc. Appl. Anal. 16 (4), 985-1008, 2013.
  • [8] J. Henderson and R. Luca, Positive solutions for a system of semipositone coupled fractional boundary value problems, Bound. Value Probl. 2016, Article No: 61, 2016.
  • [9] J. Henderson and R. Luca, Systems of Riemann-Liouville fractional equations with multi-point boundary conditions, Appl. Math. Comput. 309, 303-323, 2017.
  • [10] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, in: North-Holland Mathematics Studies 204, Elsevier Science B.V, Amsterdam, 2006.
  • [11] Y. Liu, New existence results for positive solutions of boundary value problems for coupled systems of multi-term fractional differential equations, Hacet. J. Math. Stat. 45 (2), 391-416, 2016.
  • [12] N. Nyamoradi, Multiple positive solutions for fractional differential systems, Ann Univ Ferrara 58, 359-369, 2012.
  • [13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [14] X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett. 22, 64-69, 2009.
  • [15] Y.Wang, Positive solutions for a system of fractional integral boundary value problem, Bound. Value Probl. 2013, Article No: 256, 2013.
  • [16] A. Yang and W. Ge, Positive Solutions for Boundary Value Problems of N-Dimension Nonlinear Fractional Differential System, Bound. Value Probl. 2008, Article ID 437453, 15 pages, 2008.
  • [17] A. Yang and H. Wang, Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition, Electron. J. Qual. Theory Differ. Equ. 2011 (1), 1-15, 2011.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Fulya Yoruk Deren 0000-0003-1082-7215

Publication Date December 8, 2019
IZ https://izlik.org/JA27XF75NH
Published in Issue Year 2019 Volume: 48 Issue: 6

Cite

APA Yoruk Deren, F. (2019). The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics, 48(6), 1626-1634. https://izlik.org/JA27XF75NH
AMA 1.Yoruk Deren F. The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics. 2019;48(6):1626-1634. https://izlik.org/JA27XF75NH
Chicago Yoruk Deren, Fulya. 2019. “The Multiplicity of Positive Solutions for Systems of Fractional Boundary Value Problems”. Hacettepe Journal of Mathematics and Statistics 48 (6): 1626-34. https://izlik.org/JA27XF75NH.
EndNote Yoruk Deren F (December 1, 2019) The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics 48 6 1626–1634.
IEEE [1]F. Yoruk Deren, “The multiplicity of positive solutions for systems of fractional boundary value problems”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1626–1634, Dec. 2019, [Online]. Available: https://izlik.org/JA27XF75NH
ISNAD Yoruk Deren, Fulya. “The Multiplicity of Positive Solutions for Systems of Fractional Boundary Value Problems”. Hacettepe Journal of Mathematics and Statistics 48/6 (December 1, 2019): 1626-1634. https://izlik.org/JA27XF75NH.
JAMA 1.Yoruk Deren F. The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics. 2019;48:1626–1634.
MLA Yoruk Deren, Fulya. “The Multiplicity of Positive Solutions for Systems of Fractional Boundary Value Problems”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, Dec. 2019, pp. 1626-34, https://izlik.org/JA27XF75NH.
Vancouver 1.Fulya Yoruk Deren. The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics [Internet]. 2019 Dec. 1;48(6):1626-34. Available from: https://izlik.org/JA27XF75NH