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Existence and Multiplicity of Positive Solutions for a Singular Nonlinear High Order Fractional Differential Problem with Multi-point Boundary Conditions
  
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KeyWord:Positive solutions  Fractional differential problem  Fixed point index  First eigenvalue  Multi-point boundary conditions
Author NameAffiliation
Di Wang School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China 
Jiqiang Jiang School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China 
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Abstract:
      In this paper, a singular nonlinear high order fractional differential problem involving multi-point boundary conditions is solved by means of the fixed point index theory. Some properties of the first eigenvalue corresponding to relevant operator and some new height functions are also used to prove the existence and multiplicity of positive solutions. The nonlinearity depends on arbitrary fractional derivative.