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By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by − D   0 +ν  1    y   1 ( t ) =  λ   1   a   1 ( t ) f ( y   1 ( t ),  y   2 ( t )), −  D   0 +ν  2    y   2 ( t ) =  λ   2   a   2 ( t ) g ( y   1 ( t ),  y   2 ( t )), where  D   0 +ν   is the standard Riemann-Liouville fractional derivative,  ν   1 ,  ν   2  ∈ ( n  − 1,  n ] for  n  > 3 and  n  ∈  N , subject to the boundary conditions  y   1   ( i ) (0) = 0 =  y   2   ( i ) (0), for 0 ≤  i  ≤  n  − 2, and [ D   0 +α    y   1 ( t )]  t =1  = 0 = [ D   0 +α    y   2 ( t )]  t =1 , for 1 ≤  α  ≤  n  − 2, or  y   1   ( i ) (0) = 0 =  y   2   ( i ) (0), for 0 ≤  i  ≤  n  − 2, and [ D   0 +α    y   1 ( t )]  t =1  =  ϕ   1 ( y   1 ), [ D   0 +α    y   2 ( t )]  t =1  =  ϕ   2 ( y   2 ), for 1 ≤  α  ≤  n  − 2,  ϕ   1 ,  ϕ   2  ∈  C ([0,1],  R ). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.

Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations