TY  - JOUR
T1  - The multiplicity of positive solutions for systems of  fractional boundary value problems
AU  - Yoruk Deren, Fulya
PY  - 2019
DA  - December
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1626
EP  - 1634
VL  - 48
IS  - 6
LA  - en
AB  - 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.
KW  - multiple positive solution
KW  - fractional differential equation
KW  - fixed point theorem
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [6] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
CR  - [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.
CR  - [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.
CR  - [9] J. Henderson and R. Luca, Systems of Riemann-Liouville fractional equations with
multi-point boundary conditions, Appl. Math. Comput. 309, 303-323, 2017.
CR  - [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.
CR  - [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.
CR  - [12] N. Nyamoradi, Multiple positive solutions for fractional differential systems, Ann Univ
Ferrara 58, 359-369, 2012.
CR  - [13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
CR  - [14] X. Su, Boundary value problem for a coupled system of nonlinear fractional differential
equations, Appl. Math. Lett. 22, 64-69, 2009.
CR  - [15] Y.Wang, Positive solutions for a system of fractional integral boundary value problem,
Bound. Value Probl. 2013, Article No: 256, 2013.
CR  - [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.
CR  - [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.
UR  - https://dergipark.org.tr/en/pub/hujms/issue//656651
L1  - https://dergipark.org.tr/en/download/article-file/877263
ER  -