scholarly journals Multi-term fractional boundary value problems with four-point boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Fractional Boundary Value Problems

scholarly journals Solvability for a Coupled System of Fractional Integrodifferential Equations withm-Point Boundary Conditions on the Half-Line

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Payam Nasertayoob ◽  
S. Mansour Vaezpour ◽  
Dumitru Baleanu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Coupled System ◽  
Integrodifferential Equations ◽  
Half Line ◽  
Point Boundary ◽  
Fractional Boundary Value Problems

The aim of this paper is to study the solvability for a coupled system of fractional integrodifferential equations with multipoint fractional boundary value problems on the half-line. An example is given to demonstrate the validity of our assumptions.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

Perturbation of two-point boundary value problems with eigenvalue parameter in the boundary conditions

1983 ◽  
Vol 94 (3-4) ◽  
pp. 213-219 ◽  
Author(s):  
Lawrence Turyn
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Boundary Value ◽  
Simple Eigenvalue ◽  
Point Boundary ◽  
Eigenvalue Parameter

SynopsisWe discuss smooth changes of eigenvalues under perturbation of the boundary value problems given in the title. The simple eigenvalue criterion is developed in the setting of Banach spaces, so very general perturbations of both the differential equation and the boundary conditions are allowed. Further, we need no assumptions about self-adjointness of the original or perturbed problems. The discussion is concluded with the application of the simple eigenvalue criterion to two examples.

Two point fractional boundary value problems with a fractional boundary condition

2018 ◽  
Vol 21 (2) ◽  
pp. 442-461 ◽  
Author(s):  
Jeffrey W. Lyons ◽  
Jeffrey T. Neugebauer
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

Abstract In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given.

scholarly journals Parametric quintic spline solution for sixth order two point boundary value problems

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1233-1245 ◽  
Author(s):  
Arshad Khan ◽  
Talat Sultana
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sixth Order ◽  
Point Boundary ◽  
Spline Method ◽  
Quintic Spline ◽  
Practical Usefulness ◽  
Special Case ◽  
Boundary Equations

In this paper, parametric quintic spline method is presented to solve a linear special case sixth order two point boundary value problems with two different cases of boundary conditions. The method presented in this paper has been shown to be second and fourth order accurate. Boundary equations are derived for both the cases of boundary conditions. Convergence analysis of these methods are discussed. The presented method is tested on four numerical examples of linear sixth order boundary value problems. Comparison is made to show the practical usefulness of the presented method.

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