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Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition
1.  Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, Kentucky 40475, United States, United States 
References:
[1] 
B. Ahmad and J. J. Nieto, RiemannLiouville fractional differential equations with fractional boundary conditions,, \emph{Fixed Point Theory}, 13 (2012), 329. Google Scholar 
[2] 
Z. Bai and H. Lu, Positive solutions for boundary value problems of nonlinear fractional differential equations,, \emph{J. Math. Anal. Appl.}, 311 (2005), 495. Google Scholar 
[3] 
V. DaftardarGenjji, Positive solutions of a system of nonautonomous nonlinear fractional differential equations,, \emph{J. Math. Anal. Appl.}, 302 (2004), 56. Google Scholar 
[4] 
K. Diethelm, The Analysis of Fractional Differential Equations. An Applicationoriented Exposition Using Differential Operators of Caputo Type,, Lecture Notes in Mathematics, (2004). Google Scholar 
[5] 
P. W. Eloe and J. T. Neugebauer, Conjugate points for fractional differential equations,, \emph{Fract. Calc. Appl. Anal.}, 17 (2014), 855. Google Scholar 
[6] 
P. W. Eloe, J. W. Lyons, and J. T. Neugebauer, An ordering on Green's functions for a family of twopoint boundary value problems for fractional differential equations,, \emph{Commun. Appl. Anal.}, 19 (2015), 453. Google Scholar 
[7] 
J. R. Graef and X. Liu, Existence of positive solutions of fractional boundary value problems involving bounded linear operators,, \emph{J. Nonlinear Funct. Anal.}, 2014 (2014), 1. Google Scholar 
[8] 
E. R. Kaufmann and E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation,, \emph{Electron. J. Qual. Theory Differ. Equ.}, 17 (2014), 855. Google Scholar 
[9] 
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations,, North Holland Math. Stud., (2006). Google Scholar 
[10] 
M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, (English), Translated by A. H. Armstrong,, A Pergamon Press Book, (1964). Google Scholar 
[11] 
R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces,, \emph{Indiana Univ. Math. J.}, 28 (1979), 673. Google Scholar 
[12] 
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications,, Gordon and Breach, (1993). Google Scholar 
[13] 
G. Wang, S. K. Ntouyas, and L. Zhang, Positive solutions of the threepoint boundary value problem for fractionalorder differential equations with an advanced argument,, \emph{Adv. Difference Equ.}, 2011 (2011). Google Scholar 
[14] 
S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation,, \emph{J. Math. Anal. Appl.}, 1 (2013), 12. Google Scholar 
[15] 
S. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations,, \emph{Electron. J. Diff. Eqns.}, 2006 (2006), 1. Google Scholar 
show all references
References:
[1] 
B. Ahmad and J. J. Nieto, RiemannLiouville fractional differential equations with fractional boundary conditions,, \emph{Fixed Point Theory}, 13 (2012), 329. Google Scholar 
[2] 
Z. Bai and H. Lu, Positive solutions for boundary value problems of nonlinear fractional differential equations,, \emph{J. Math. Anal. Appl.}, 311 (2005), 495. Google Scholar 
[3] 
V. DaftardarGenjji, Positive solutions of a system of nonautonomous nonlinear fractional differential equations,, \emph{J. Math. Anal. Appl.}, 302 (2004), 56. Google Scholar 
[4] 
K. Diethelm, The Analysis of Fractional Differential Equations. An Applicationoriented Exposition Using Differential Operators of Caputo Type,, Lecture Notes in Mathematics, (2004). Google Scholar 
[5] 
P. W. Eloe and J. T. Neugebauer, Conjugate points for fractional differential equations,, \emph{Fract. Calc. Appl. Anal.}, 17 (2014), 855. Google Scholar 
[6] 
P. W. Eloe, J. W. Lyons, and J. T. Neugebauer, An ordering on Green's functions for a family of twopoint boundary value problems for fractional differential equations,, \emph{Commun. Appl. Anal.}, 19 (2015), 453. Google Scholar 
[7] 
J. R. Graef and X. Liu, Existence of positive solutions of fractional boundary value problems involving bounded linear operators,, \emph{J. Nonlinear Funct. Anal.}, 2014 (2014), 1. Google Scholar 
[8] 
E. R. Kaufmann and E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation,, \emph{Electron. J. Qual. Theory Differ. Equ.}, 17 (2014), 855. Google Scholar 
[9] 
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations,, North Holland Math. Stud., (2006). Google Scholar 
[10] 
M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, (English), Translated by A. H. Armstrong,, A Pergamon Press Book, (1964). Google Scholar 
[11] 
R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces,, \emph{Indiana Univ. Math. J.}, 28 (1979), 673. Google Scholar 
[12] 
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications,, Gordon and Breach, (1993). Google Scholar 
[13] 
G. Wang, S. K. Ntouyas, and L. Zhang, Positive solutions of the threepoint boundary value problem for fractionalorder differential equations with an advanced argument,, \emph{Adv. Difference Equ.}, 2011 (2011). Google Scholar 
[14] 
S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation,, \emph{J. Math. Anal. Appl.}, 1 (2013), 12. Google Scholar 
[15] 
S. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations,, \emph{Electron. J. Diff. Eqns.}, 2006 (2006), 1. Google Scholar 
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