One-sided and two-sided Green’s functions

Boundary value problems

Rubens de Figueiredo Camargo¹  Edmundo Capelas de Oliveira²  Ary Orozimbo Chiacchio³ 

[1] Departamento de Matemáncias, Unesp, Bauru, Brazil;tica, Faculdade de Ciêtica, Imecc, Unicamp, Campinas, Brazil

关键词: Ordinary Differential Equation;    Constant Coefficient;    Fractional Differential Equation;    Homogeneous Boundary Condition;    Fractional Partial Differential Equation;   

DOI  :  10.1186/1687-2770-2013-45

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We discuss the one-sided Green’s function, associated with an initial value problem and the two-sided Green’s function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green’s functions and conclude which is the most convenient one. An incursion in the so-called fractional Green’s function is also presented. As an example, we discuss the isotropic harmonic oscillator.

【 授权许可】

CC BY