On positive solutions for a m-point fractional boundary value problem on an infinite interval

被引：0
作者：
J. Caballero
J. Harjani
K. Sadarangani
机构：
[1] Universidad de Las Palmas de Gran Canaria,Departamento de Matemáticas
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2019年 / 113卷
关键词：
m-point fractional boundary value problem; Fixed point theorem; Positive solution; 47H10; 49L20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, by using a recent fixed point theorem, we study the existence and uniqueness of positive solutions for the following m-point fractional boundary value problem on an infinite interval D0+αx(t)+f(t,x(t))=0,0<t<∞,x(0)=x′(0)=0,D0+α-1x(+∞)=∑i=1m-2βix(ξi),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left\{ \begin{array}{ll} D_{0^{+}}^{\alpha }x(t)+f(t,x(t))=0,&{}\quad 0<t<\infty ,\\ x(0)=x'(0)=0,&{}\quad D_{0^{+}}^{\alpha -1}x(+\infty )= \sum _{i=1}^{m-2}\beta _{i}x(\xi _{i}), \end{array} \right. \end{aligned}$$\end{document}where 2<α<3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2<\alpha <3$$\end{document}, D0+α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{0^{+}}^{\alpha }$$\end{document} is the standard Riemann-Liouville fractional derivative, D0+α-1x(+∞)=limt→∞D0+α-1x(t),0<ξ1<ξ2<⋯<ξm-2<∞andβi≥0fori=1,2,…,m-2.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&D_{0^{+}}^{\alpha -1}x(+\infty )=\displaystyle \lim _{t\rightarrow \infty }D_{0^{+}}^{\alpha -1}x(t),\\&0<\xi _{1}<\xi _{2}<\cdots<\xi _{m-2}<\infty \quad \text {and} \quad \beta _{i}\ge 0 \quad for \quad i=1,2,\ldots ,m-2. \end{aligned}$$\end{document}Moreover, we present an example illustrating our results.
引用
收藏
页码：3635 / 3647
页数：12
相关论文
共 22 条
[1]  
Zima M(2001)On positive solution of boundary value problems on the half-line J. Math. Anal. Appl. 259 127-136
[2]  
Lian H(2007)Triple positive solutions for boundary value problems on infinite intervals Nonlinear Anal. 67 2199-2207
[3]  
Pang H(2011)Unbounded solutions to a boundary value problem of fractional order on the half-line Comput. Math. Appl. 61 1079-1087
[4]  
Ge W(2010)Fractional order differential equations on an unbounded domain Nonlinear Anal. 72 580-586
[5]  
Su X(2011)Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval Math. Comput. Model. 54 1334-1346
[6]  
Zhang S(2011)Existence of three positive solutions of m-point boundary value problems for some nonlinear fractional differential equations on an infinite interval Comput. Math. Appl. 61 3343-3354
[7]  
Arara A(2013)Upper and lower method for fractional boundary value problems on the half-line J. Appl. Math. 2013 11-1298
[8]  
Benchohra M(2015)On the existence of solution to a boundary value problem of fractional differential equation on the infinite interval Bound. Value Probl. 2015 241-undefined
[9]  
Hamidi N(2019)Properties of positive solutions for m-point fractional differential equations on an infinite interval RACSAM 113 1289-undefined
[10]  
Nieto J(2012)Fixed points of a new type of contractive mappings in complete metric spaces Fixed Point Theory Appl. 2012 14-undefined
123