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This work is concerned with the existence and uniqueness of positive solutions for the following fractional boundary value problem: {-D 0+ νy(t) = f (t, y(t), y(t)) + g(t, y(t)), 0 < t < 1, n - 1 < ν ≤ n, y(i)(0) = 0, 0 ≤ i ≤ n - 2, [D 0+ α y(t)]t=1 = 0, 1 ≤ α ≤ n - 2, where D0+ ν is the standard Riemann-Liouville fractional derivative of order ν, and n ε N, n > 3. Our analysis relies on two new fixed point theorems for mixed monotone operators with perturbation. Our results can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate the main result. © 2013 Zhai and Hao;.

boundary value problems

Mixed monotone operator methods for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems