The uniqueness of positive solution for a singular fractional differential system involving derivatives

By using the fixed point theorem of the mixed monotone operator, the uniqueness of positive solution for a singular fractional differential system involving derivatives is established. An example is then given to illuminate the application of the main results.

[1]  Existence results for higher order fractional differential inclusions with nonlocal boundary conditions , 2010 .

[2]  Xinguang Zhang,et al.  Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations , 2012, Appl. Math. Lett..

[3]  Christopher S. Goodrich,et al.  Positive solutions to boundary value problems with nonlinear boundary conditions , 2012 .

[4]  Rahmat Ali Khan,et al.  Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations , 2010, Appl. Math. Lett..

[5]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[6]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[7]  Yonghong Wu,et al.  Multiple positive solutions of a singular fractional differential equation with negatively perturbed term , 2012, Math. Comput. Model..

[8]  Socio Michele Caputo.  Free modes splitting and alterations of electrochemically polarizable media , 1993 .

[9]  Christopher S. Goodrich,et al.  Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions , 2011, Comput. Math. Appl..

[10]  C. F. Li,et al.  Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations , 2010, Comput. Math. Appl..

[11]  Bashir Ahmad,et al.  Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions , 2009, Comput. Math. Appl..

[12]  Weihua Jiang,et al.  The existence of solutions to boundary value problems of fractional differential equations at resona , 2011 .

[13]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[14]  Hussein A. H. Salem,et al.  On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies , 2009 .