As we know one of the most important equations which have many applications in various areas physics, mathematics, and financial markets, is Sturm–Liouville equation. In this paper, by using α-ψ-contraction technique fixed point theory employing some functional inequalities, study existence solutions partial fractional hybrid case generalized Sturm–Liouville-Langevin under boundary value condit...

We study finite difference approximations of solutions of direct and inverse Sturm–Liouville problems, in a finite or infinite interval on the real line. The discretization is done on optimal grids, with a three-point finite difference stencil. The optimal location of the grid points is calculated via a rational approximation of the Neumann-to-Dirichletmap and the latter converges exponentially...

This work develops scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with parameter in boundary condition. Giving the Jost solution solutions this problem, we find function problem. Discussing properties function, solutions, asymptotic behavior solution, Green resolvent operator, continuous point spectrum Finally, give an example which main results are made expli...

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

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 study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.