Boundary value problem for p-Laplacian Caputo fractional difference equations with fractional sum boundary conditions

In this paper, we consider a discrete fractional boundary value problem of the form (t)=f(t++-1,x(t++-1)), t[0,T]N0, C x(-1)=0,x(++T)=-x(+), where 0 < ,1, 1 < + 2, 0 < 1, [+-1,T++-1] N+-1, is a constant, and denote the Caputo fractional differences of order and , respectively, f:<mml:msub>[+-2,T++] N+-2xRR is a continuous function, and phi(p) is the p-Laplacian operator. The existence of at least one solution is proved by using Banach fixed point theorem and Schaefer's fixed point theorem. Some illustrative examples are also presented. Copyright (c) 2015 John Wiley & Sons, Ltd.