In this paper, we give sufficient conditions for the existence and uniqueness of solution Sturm–Liouville equations subject to Dirichlet boundary value involving Kurzweil–Henstock integrable functions on unbounded intervals. We also present a finite element method scheme functions.

In this a paper perturbations of multiple eigenvalues Schmidt spectral problems is considered. At the usage reductional method suggested in articles [11, 12] investigation perturbation reduced to simple ones. end, as application obtained results problem about boundary for system two Sturm–Liouville with parameter

This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...

This work is concerned with the computation of eigenvalues and eigenfunctions of singular eigenvalue problems (EVPs) arising in ordinary differential equations. Two different numerical methods to determine values for the eigenparameter such that the boundary value problem has nontrivial solutions are considered. The first approach incorporates a collocation method. In the course of this work th...

We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α ∈ (3/2, 2) on the unit interval (0, 1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα−1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value pro...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...