Abstract

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

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