An efficient method for solving fractional Sturm–Liouville problems

2009 ◽  
Vol 40 (1) ◽  
pp. 183-189 ◽  
Author(s):  
Qasem M. Al-Mdallal
Keyword(s):  
Efficient Method ◽  
Sturm Liouville

scholarly journals Some notes on conformable fractional Sturm–Liouville problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wei-Chuan Wang
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Efficient Method ◽  
Sturm Liouville

AbstractThe conformable fractional eigenvalue problem $$\begin{aligned} -D_{x}^{\alpha }D_{x}^{\alpha }y+q(x)y=\lambda \rho (x)y \end{aligned}$$ − D x α D x α y + q ( x ) y = λ ρ ( x ) y is considered. We employ an easy and efficient method to derive its eigenvalue asymptotic expansion. On the basis of this result, we also investigate Ambarzumyan problems related to this eigenvalue problem as an application.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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