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In this paper, we investigate the existence of three positiv e solutions for the nonlinear fractional boundary value problem D + u(t) + a(t) f (t, u(t), u 00 (t)) = 0, 0 < t < 1, 3 <   4, u(0) = u 0 (0) = u 00 (0) = u 00 (1) = 0, where D + is the standard Riemann-Liouville fractional derivative. The method involves applications of a new fixed-point theorem due to Bai and Ge. The interesting point l ies in the fact that the nonlinear term is allowed to depend on the second order derivative u 00 .

Triple positive solutions for a boundary value problem of nonlinear fractional differential equation