scholarly journals Green’s function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Jie Zhou ◽  
Meiqiang Feng
Keyword(s):  
Differential Equations ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Green's Function ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Type Boundary

scholarly journals Note on the conformable boundary value problems: Sturm’s theorems and Green’s function

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 471
Author(s):  
F. Martínez ◽  
I. Martínez ◽  
M. K. A. Kaabar ◽  
S. Paredes
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Liouville Problem ◽  
Comparison Theorems ◽  
Conformable Derivative ◽  
Sturm Liouville ◽  
Linear Differential

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

scholarly journals Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function

2020 ◽  
Author(s):  
F. Martínez ◽  
Inmaculada Martínez ◽  
Mohammed K. A. Kaabar ◽  
Silvestre Paredes
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Liouville Problem ◽  
Comparison Theorems ◽  
Conformable Derivative ◽  
Sturm Liouville ◽  
Linear Differential

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

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