Existence results for a discrete fractional boundary value problem driven by p-Laplacian operator

Global optimization concentrates on finding the maximum or mini- mum over all input values. Optimization problems are ubiquitous in the mathematical modeling of real-world systems and cover a very broad range of applications arising in all branches of economics, finance, chemistry, materials science, astronomy, physics, structural and molec- ular biology, engineering, computer science, and medicine. In this paper, we shall discuss the existence of at least one weak solution and infinitely many weak solutions for a discrete fractional bound- ary value problems driven by p-Laplacian operator. In particular, in our work, we shall look for local minima for the Euler functional cor- responding to discrete fractional boundary value problems involving p-Laplacian. On the other hand, equations involving the discrete p- Laplacian operator, subjected to classical or less classical boundary conditions, have been widely studied by many authors using various tech- niques. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, some examples are presented to demonstrate the application of our main results.