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Existence of nontrivial solutions to systems of multipoint boundary value problems
Positive solutions of nonlocal fractional boundary value problems
1.  Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States, United States 
2.  Department of Mathematics, Northern Illinois University, DeKalb, Il 60115 
References:
[1] 
R. Agarwal, D. O'Regan, and S. Staněk, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations,, J. Math. Anal. Appl. 371 (2010), 371 (2010), 57. Google Scholar 
[2] 
B. Ahmad and J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with threepoint boundary conditions,, Comput. Math. Appl. 58 (2009), 58 (2009), 1838. Google Scholar 
[3] 
Z. Bai and H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation,, J. Math. Anal. Appl. 311 (2005), 311 (2005), 495. Google Scholar 
[4] 
K. Deimling, "Nonlinear Functional Analysis'',, SpringerVerlag, (1985). Google Scholar 
[5] 
M. Feng, X. Zhang, and W. Ge, New existence results for higherorder nonlinear fractional differential equation with integral boundary conditions,, Bound. Value Probl. (2011), (2011). Google Scholar 
[6] 
C. Goodrich, Existence of a positive solution to a class of fractional differential equations,, Appl. Math. Lett. 23 (2010), 23 (2010), 1050. Google Scholar 
[7] 
J. R. Graef, L. Kong, Q. Kong, and M. Wang, Fractional boundary value problems with integral boundary conditions,, Appl. Anal. 92 (2013), 92 (2013), 2008. Google Scholar 
[8] 
D. Guo and V. Lakshmikantham, "Nonlinear Problems in Abstract Cones'',, Academic Press, (1988). Google Scholar 
[9] 
R. Hilfer, "Applications of Fractional Calculus in Physics'',, World Scientific, (2000). Google Scholar 
[10] 
D. Jiang and C. Yuan, The positive properties of the Green function for Dirichlettype boundary value problems of nonlinear fractional differential equations and its application,, Nonlinear Anal. 72 (2010), 72 (2010), 710. Google Scholar 
[11] 
Q. Kong and M. Wang, Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions,, Electron. J. Qual. Theory Differ. Equ., (2012), 1. Google Scholar 
[12] 
V. Tarasov, "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media'',, SpringerVerlag, (2011). Google Scholar 
[13] 
L. Yang and H. Chen, Unique positive solutions for fractional differential equation boundary value problems,, Appl. Math. Lett. 23 (2010), 23 (2010), 1095. Google Scholar 
[14] 
W. Yang, Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions,, Comput. Math. Appl. 63 (2012), 63 (2012), 288. Google Scholar 
[15] 
E. Zeidler, "Nonlinear Functional Analysis and its Applications I: FixedPoint Theorems'',, SpringerVerlag, (1986). Google Scholar 
[16] 
C. Zhai and M. Hao, Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems,, Nonlinear Anal., 75 (2012), 2542. Google Scholar 
[17] 
S. Zhang, Positive solutions to singular boundary value problem for nonlinear fractional differential equation,, Comput. Math. Appl. 59 (2010), 59 (2010), 1300. Google Scholar 
show all references
References:
[1] 
R. Agarwal, D. O'Regan, and S. Staněk, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations,, J. Math. Anal. Appl. 371 (2010), 371 (2010), 57. Google Scholar 
[2] 
B. Ahmad and J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with threepoint boundary conditions,, Comput. Math. Appl. 58 (2009), 58 (2009), 1838. Google Scholar 
[3] 
Z. Bai and H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation,, J. Math. Anal. Appl. 311 (2005), 311 (2005), 495. Google Scholar 
[4] 
K. Deimling, "Nonlinear Functional Analysis'',, SpringerVerlag, (1985). Google Scholar 
[5] 
M. Feng, X. Zhang, and W. Ge, New existence results for higherorder nonlinear fractional differential equation with integral boundary conditions,, Bound. Value Probl. (2011), (2011). Google Scholar 
[6] 
C. Goodrich, Existence of a positive solution to a class of fractional differential equations,, Appl. Math. Lett. 23 (2010), 23 (2010), 1050. Google Scholar 
[7] 
J. R. Graef, L. Kong, Q. Kong, and M. Wang, Fractional boundary value problems with integral boundary conditions,, Appl. Anal. 92 (2013), 92 (2013), 2008. Google Scholar 
[8] 
D. Guo and V. Lakshmikantham, "Nonlinear Problems in Abstract Cones'',, Academic Press, (1988). Google Scholar 
[9] 
R. Hilfer, "Applications of Fractional Calculus in Physics'',, World Scientific, (2000). Google Scholar 
[10] 
D. Jiang and C. Yuan, The positive properties of the Green function for Dirichlettype boundary value problems of nonlinear fractional differential equations and its application,, Nonlinear Anal. 72 (2010), 72 (2010), 710. Google Scholar 
[11] 
Q. Kong and M. Wang, Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions,, Electron. J. Qual. Theory Differ. Equ., (2012), 1. Google Scholar 
[12] 
V. Tarasov, "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media'',, SpringerVerlag, (2011). Google Scholar 
[13] 
L. Yang and H. Chen, Unique positive solutions for fractional differential equation boundary value problems,, Appl. Math. Lett. 23 (2010), 23 (2010), 1095. Google Scholar 
[14] 
W. Yang, Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions,, Comput. Math. Appl. 63 (2012), 63 (2012), 288. Google Scholar 
[15] 
E. Zeidler, "Nonlinear Functional Analysis and its Applications I: FixedPoint Theorems'',, SpringerVerlag, (1986). Google Scholar 
[16] 
C. Zhai and M. Hao, Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems,, Nonlinear Anal., 75 (2012), 2542. Google Scholar 
[17] 
S. Zhang, Positive solutions to singular boundary value problem for nonlinear fractional differential equation,, Comput. Math. Appl. 59 (2010), 59 (2010), 1300. Google Scholar 
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