| | | |

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

#### Fulya YORUK DEREN [1]

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.
multiple positive solution, fractional differential equation, fixed point theorem
• [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.
Primary Language en Mathematics Mathematics Orcid: 0000-0003-1082-7215Author: Fulya YORUK DEREN (Primary Author)Institution: EGE UNIVERSITY, FACULTY OF SCIENCECountry: Turkey Publication Date : December 8, 2019
 Bibtex @research article { hujms656651, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1626 - 1634}, doi = {}, title = {The multiplicity of positive solutions for systems of fractional boundary value problems}, key = {cite}, author = {YORUK DEREN, Fulya} } 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 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/50516/656651 MLA YORUK DEREN, F . "The multiplicity of positive solutions for systems of fractional boundary value problems". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1626-1634 Chicago YORUK DEREN, F . "The multiplicity of positive solutions for systems of fractional boundary value problems". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1626-1634 RIS TY - JOUR T1 - The multiplicity of positive solutions for systems of fractional boundary value problems AU - Fulya YORUK DEREN Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1626 EP - 1634 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics The multiplicity of positive solutions for systems of fractional boundary value problems %A Fulya YORUK DEREN %T The multiplicity of positive solutions for systems of fractional boundary value problems %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R %U 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 . AMA 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. 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): 1634-1626.