Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 8 1 2024 02 20 A Survey on Existence of a Solution to Singular Fractional Difference Equation 10 18 395 10.22128/gadm.2024.764.1101 EN Mohsen Khaleghi Moghdam Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, Sari, Iran Journal Article 2023 12 20 ‎In this paper‎, ‎we deal with the existence of a positive solution for the‎<br />‎following fractional discrete boundary-value problem‎<br />‎\begin{equation*}‎<br />‎\begin{cases}‎<br />‎_{T+1}\nabla_k^{\alpha}\left( ^{}_k\nabla_{0}^{\alpha}(u(k))\right)=\lambda f(k,u(k))‎, ‎\ \ k \in [1,T]_{\mathbb{N}_{0}},\\‎<br />‎u(0)= u(T+1)=0‎,<br />‎\end{cases}‎<br />‎\end{equation*}‎<br />‎where $0< \alpha<1$ and $^{}_k\nabla_{0}^{\alpha}$ is the left nabla discrete fractional difference and $^{}_{T+1}\nabla_k^{\alpha}$ is the right nabla discrete fractional difference $f‎: ‎[1,T]_{\mathbb{N}_{0}}\times (0,+\infty)\to\mathbb{R}$ may be singular at $t=0$ and may change sign and $\lambda>0$ is a parameter‎. ‎The technical method is variational approach for differentiable functionals‎. ‎An example is included to illustrate the main results. Discrete fractional calculus Discrete nonlinear boundary value problem Non trivial solution Variational methods Critical point theory https://ansne.du.ac.ir/article_395_19fa3cc09a3bbbcaac9fcc7fa51e3984.pdf