The main aim of this paper is to construct quantum extension of the discrete Sturm–Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. ...

This paper deals with a class of nonlinear fractional Sturm–Liouville boundary value problems. Each sub equation in the system is partial including second kinds Fredholm integral and p-Laplacian operator, simultaneously. Infinitely many solutions are derived due to perfect involvements calculus theory variational methods some simpler more easily verified assumptions.