Solvability of boundary-value problems for nonlinear fractional differential equations

We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations

*20c Da u(t) + l f( t,u(t) ) + q(t) ] = 0,    0 < t < 1, u(0) = 0,    u(1) = bu(h), \begin{array}{*{20}{c}} {{{\mathbf{D}}^\alpha }u(t) + {{\lambda }}\left {f\left( {t,u(t)} \right) + q(t)} \right] = 0,\quad 0 < t < 1,} \\ {u(0) = 0,\quad u(1) = \beta u(\eta ),} \\ \end{array}
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