Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators

We consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g...

Full description

Saved in:
Bibliographic Details
Main Authors: Dongyuan Liu, Zigen Ouyang, Huilan Wang
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2015/263748
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832547406306082816
author Dongyuan Liu
Zigen Ouyang
Huilan Wang
author_facet Dongyuan Liu
Zigen Ouyang
Huilan Wang
author_sort Dongyuan Liu
collection DOAJ
description We consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g(t,u):[0,1]×[0,∞)→[0,∞), and g(0,0)=0 the function f is defined as f(t,u):[0,1]×[0,∞)→[0,∞)σ(t), τ(t) are continuous on t and 0≤σ(t), τ(t)≤t. Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.
format Article
id doaj-art-0c2b8efcaa144ecf86ecc33b0bf7fc8d
institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2015-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-0c2b8efcaa144ecf86ecc33b0bf7fc8d2025-02-03T06:44:51ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/263748263748Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential OperatorsDongyuan Liu0Zigen Ouyang1Huilan Wang2School of Mathematics and Physics, University of South China, Hengyang 421001, ChinaSchool of Mathematics and Physics, University of South China, Hengyang 421001, ChinaSchool of Mathematics and Physics, University of South China, Hengyang 421001, ChinaWe consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g(t,u):[0,1]×[0,∞)→[0,∞), and g(0,0)=0 the function f is defined as f(t,u):[0,1]×[0,∞)→[0,∞)σ(t), τ(t) are continuous on t and 0≤σ(t), τ(t)≤t. Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.http://dx.doi.org/10.1155/2015/263748
spellingShingle Dongyuan Liu
Zigen Ouyang
Huilan Wang
Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
Abstract and Applied Analysis
title Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
title_full Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
title_fullStr Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
title_full_unstemmed Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
title_short Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
title_sort positive solutions for class of state dependent boundary value problems with fractional order differential operators
url http://dx.doi.org/10.1155/2015/263748
work_keys_str_mv AT dongyuanliu positivesolutionsforclassofstatedependentboundaryvalueproblemswithfractionalorderdifferentialoperators
AT zigenouyang positivesolutionsforclassofstatedependentboundaryvalueproblemswithfractionalorderdifferentialoperators
AT huilanwang positivesolutionsforclassofstatedependentboundaryvalueproblemswithfractionalorderdifferentialoperators