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.