a survey on existence of a solution to singular fractional difference equation

In this paper, we deal with the existence of a positive solution for the following fractional discrete boundary-value problemt+1∇αk(k∇α0(uk)))=λƒ(k,u(k)), k∈[1,t]n0,u(0)=u (t+1)=0,where 0<α<1 and k∇α0 is the left nabla discrete fractional difference and t+1∇αk is the right nabla discrete fractional difference ƒ:[1,t]n0×(0,+∞)→r may be singular at t=0  and may change sign and λ>0 is a parameter. the technical method is variational approach for differentiable functionals. an example is included to illustrate the main results.