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

Year 2019, Volume: 48 Issue: 6, 1626 - 1634, 08.12.2019

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

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 Mathematics
Authors

Fulya Yoruk Deren 0000-0003-1082-7215

Publication Date December 8, 2019
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.
AMA Yoruk Deren F. The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics. December 2019;48(6):1626-1634.
Chicago Yoruk Deren, Fulya. “The Multiplicity of Positive Solutions for Systems of Fractional Boundary Value Problems”. Hacettepe Journal of Mathematics and Statistics 48, no. 6 (December 2019): 1626-34.
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 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, 2019.
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 2019), 1626-1634.
JAMA 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, 2019, pp. 1626-34.
Vancouver Yoruk Deren F. The multiplicity of positive solutions for systems of fractional boundary value problems. Hacettepe Journal of Mathematics and Statistics. 2019;48(6):1626-34.