POSITIVE SOLUTIONS OF A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION BOUNDARY VALUE PROBLEM

2018 ◽  
Vol 19 (4) ◽  
pp. 369-389
Author(s):  
Yan Sun
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Nonlinear Fractional Differential Equation ◽  
Equation Boundary ◽  
Fractional Differential

scholarly journals Existence of Positive Solutions to Boundary Value Problem of Caputo Fractional Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yaqiong Cui ◽  
Shugui Kang ◽  
Zhiping Liu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Nonlinear Fractional Differential Equation ◽  
Equation Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Interior Points

We consider the existence of positive solutions to the nonlinear fractional differential equation boundary value problemD0+αCut+fut,u't=0,  t∈0,1,  u0=u1=u″0=0, wheref:0,+∞×R→0,+∞is continuous,α∈2,3, andD0+αCis the standard Caputo differentiation. By using fixed point theorems on cone, we give some existence results concerning positive solutions. Here the solutions especially are the interior points of cone.

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