Existence of solutions for a higher order fractional boundary value problem posed on the half-line

2019 ◽  
Vol 12 (01) ◽  
pp. 1950008
Author(s):  
A. Boucenna ◽  
T. Moussaoui
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Monotone Operators ◽  
Higher Order ◽  
Half Line ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Continuous Embedding

The aim of this paper is to study the existence and uniqueness of solutions for a boundary value problem associated with a fractional nonlinear differential equation with higher order posed on the half-line. An appropriate continuous embedding for suitable Banach spaces are proved and the Minty–Browder theorem for monotone operators is used in the proof of existence of solutions for a boundary value problem of fractional order posed on the half-line.

A boundary value problem on the half-line for higher-order nonlinear differential equations

2009 ◽  
Vol 139 (5) ◽  
pp. 1017-1035 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Higher Order ◽  
Half Line ◽  
Nonlinear Ordinary Differential Equations ◽  
Specific Class

This article is devoted to the study of the existence of solutions as well as the existence and uniqueness of solutions to a boundary-value problem on the half-line for higher-order nonlinear ordinary differential equations. An existence result is obtained by the use of the Schauder–Tikhonov theorem. Furthermore, an existence and uniqueness criterion is established using the Banach contraction principle. These two results are applied, in particular, to the specific class of higher-order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of higher-order linear ordinary differential equations, respectively. Moreover, some (general or specific) examples demonstrating the applicability of our results are given.

scholarly journals Existence and uniqueness of solutions for a fractional boundary value problem on a graph

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Point Theory ◽  
Star Graph ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions

AbstractIn this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

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