Computation of positive solutions for nonlinear fractional q-difference equations with nonlocal conditions

In this paper, we discuss the existence of positive solutions for a nonlinear fractional q-difference equations boundary value problem {(D^α_qu)(t) + a(t)f(u(t))=0, 0<;t<;1, u(0) = (D_qu)(0) = 0, (D_qu)(1) = βu(η), where 0 <; q <; 1, 2 <; α ≤ 3, 0 <; η <; 1, 0 <; βη^α-1 <; [α-1]_q, by applying a fixed point theorem on cone. At last, we give an example to illuminate the results by computation.