In this paper, we deal with the existence of a positive solution for the following fractional discrete boundary-value problem T+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.
Khaleghi Moghdam, M. (2023). A Survey on Existence of a Solution to Singular Fractional Difference Equation. Analytical and Numerical Solutions for Nonlinear Equations, 8(1), 11-21. doi: 10.22128/gadm.2024.764.1101
MLA
Mohsen Khaleghi Moghdam. "A Survey on Existence of a Solution to Singular Fractional Difference Equation", Analytical and Numerical Solutions for Nonlinear Equations, 8, 1, 2023, 11-21. doi: 10.22128/gadm.2024.764.1101
HARVARD
Khaleghi Moghdam, M. (2023). 'A Survey on Existence of a Solution to Singular Fractional Difference Equation', Analytical and Numerical Solutions for Nonlinear Equations, 8(1), pp. 11-21. doi: 10.22128/gadm.2024.764.1101
VANCOUVER
Khaleghi Moghdam, M. A Survey on Existence of a Solution to Singular Fractional Difference Equation. Analytical and Numerical Solutions for Nonlinear Equations, 2023; 8(1): 11-21. doi: 10.22128/gadm.2024.764.1101
)