标题：Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p -Laplacian operator
摘要：In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: D q γ ( ϕ p ( D q δ y ( t ) ) ) + f ( t , y ( t ) ) = 0 $D_{q}^{\gamma}(\phi_{p}(D_{q}^{\delta}y(t)))+f(t,y(t))=0$ ( 0 < t < 1 $0< t<1$ ; 0 < γ < 1 $0<\gamma<1$ ; 3 < δ < 4 $3<\delta<4$ ), y ( 0 ) = ( D q y ) ( 0 ) = ( D q 2 y ) ( 0 ) = 0 $y(0)=(D_{q}y)(0)=(D_{q}^,y)(0) =0$ , a 1 ( D q y ) ( 1 ) + a 2 ( D q 2 y ) ( 1 ) = 0 $a_)(D_{q}y)(1)+a_,(D_{q}^,y)(1)=0$ , a 1 + a 2 ≠ 0 $a_) +\vert a_,\vert \neq0$ , D 0 + γ y ( t ) t = 0 = 0 $D_{0+}^{\gamma}y(t) _{t=0}=0$ . We make use of such a fractional q-difference boundary value problem in order to show the existence and uniqueness of positive and nondecreasing solutions by means of a familiar fixed point theorem.
关键词：positive solutions ; fixed point theorem ; fractional q -difference equation ; p -Laplacian operator
