New classes of Lyapunov type inequalities of fractional $Delta$-difference Sturm-Liouville problems with applications

Inequalities among eigenvalues of Sturm-Liouville problems

On the numerical solution of fractional Sturm-Liouville problems

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to da...

Sturm-liouville Problems

Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.

A New Proof of the Inequalities among Sturm-Liouville Eigenvalues

We consider self-adjoint regular Sturm-Liouville problems with positive leading coefficients and weight functions. A new proof of the inequalities among the eigenvalues for separated boundary conditions and those for coupled boundary conditions established recently by three of the authors with M. S. P. Eastham is given. This new proof does not assume that any special case of the inequalities ha...

Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation

Article history: Received 11 March 2013 Received in revised form 25 June 2013 Accepted 27 June 2013 Available online 4 July 2013

Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.