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The authors use the mixed monotone operator method to study the fractional boundary value problem −D ν+ u(t )= λ f (t, u), t ∈ (0,1), u (j) (0 )= 0, j = 0,...,n −2, (D α+ u(t))t=1 = 0. Here, m 1a ndn 3 are integers, n −1 < ν n ,1 α n −2, u(t)=(u1(t),...,um(t)) T , λ =(λ1,...,λm), λ f (t, u)=(λ1 f1(t, u),...,λm fm(t, u)) T ,a ndD ν+ is the Riemann-Liouville fractional derivative of order ν . Existence, uniqueness, and dependence of positive solutions on the parameter λ are discussed. An application to a special problem is also presented.

Application of the mixed monotone operator method to fractional boundary value problems