A Survey on Existence of a Solution to Singular Fractional Difference Equation

Document Type : Research Paper


Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, Sari, Iran



In this paper, we deal with the existence of a positive solution for the following fractional discrete boundary-value problem
T+1αk(kα0(UK)))=λƒ(K,U(K)), k∈[1,T]N0,
u(0)=u (T+1)=0,

where 0<α<1 and kα0 is the left nabla discrete fractional difference and T+1αk 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.