A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained.

‎in this paper‎, ‎we formulate the sixth-order boundary value problem as fredholm integral equation by finding green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎also nonexistence results are obtained‎. ‎an example is given to illustrate the results of paper‎.

abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some exi...

Oscillation and nonoscillation properties of second order Sturm–Liouville dynamic equations on time scales attracted much interest. These equations include, as special cases, second order self-adjoint differential equations as well as second order Sturm–Liouville difference equations. In this paper we consider a given (homogeneous) equation and a corresponding equation with forcing term. We giv...

the purpose of this article is to use the classical sampling theorem, wks sampling theorem, to deriveapproximate values of the eigenvalues of the sturm-liouville problems with eigenparameter in the boundaryconditions. error analysis is used to give estimates of the associated error. higher order approximations are also drived, which lead to more complicated computations. we give some examples a...