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[ {fleft( {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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