Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation

Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation

In this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least o...

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Main Authors: Xiaoyan Dou, Yongkun Li, Ping Liu
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2011-01-01
Series:Opuscula Mathematica
Subjects:
four-point boundary value problem
Riemann-Liouville fractional derivative
Green's function
Schauder fixed-point theorem
Online Access:http://www.opuscula.agh.edu.pl/vol31/3/art/opuscula_math_3125.pdf
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spelling doaj-d19689667a42484ab61e907f11333cff2020-11-24T22:43:52ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742011-01-01313359372http://dx.doi.org/10.7494/OpMath.2011.31.3.3593125Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equationXiaoyan Dou0Yongkun Li1Ping Liu2Yunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. ChinaYunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. ChinaYunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. ChinaIn this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for the problem by using the Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered to the equivalent Fredholm integral equation.http://www.opuscula.agh.edu.pl/vol31/3/art/opuscula_math_3125.pdffour-point boundary value problemRiemann-Liouville fractional derivativeGreen's functionSchauder fixed-point theorem
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoyan Dou
Yongkun Li
Ping Liu
spellingShingle Xiaoyan Dou
Yongkun Li
Ping Liu
Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
Opuscula Mathematica
four-point boundary value problem
Riemann-Liouville fractional derivative
Green's function
Schauder fixed-point theorem
author_facet Xiaoyan Dou
Yongkun Li
Ping Liu
author_sort Xiaoyan Dou
title Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
title_short Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
title_full Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
title_fullStr Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
title_full_unstemmed Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
title_sort existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2011-01-01
description In this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for the problem by using the Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered to the equivalent Fredholm integral equation.
topic four-point boundary value problem
Riemann-Liouville fractional derivative
Green's function
Schauder fixed-point theorem
url http://www.opuscula.agh.edu.pl/vol31/3/art/opuscula_math_3125.pdf
work_keys_str_mv AT xiaoyandou existenceofsolutionsforafourpointboundaryvalueproblemofanonlinearfractionaldifferentialequation
AT yongkunli existenceofsolutionsforafourpointboundaryvalueproblemofanonlinearfractionaldifferentialequation
AT pingliu existenceofsolutionsforafourpointboundaryvalueproblemofanonlinearfractionaldifferentialequation
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