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.
[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
[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.
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.