$Existence of solutions for a mixed fractional boundary value problem$

Existence of solutions for a mixed fractional boundary value problem

Abstract In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii’s fixed point theorem to...

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Main Authors:	A Guezane Lakoud, R Khaldi, Adem Kılıçman
Format:	Article
Language:	English
Published:	SpringerOpen 2017-06-01
Series:	Advances in Difference Equations
Subjects:	boundary value problem fractional derivative fixed point theorem existence of solution integral equation
Online Access:	http://link.springer.com/article/10.1186/s13662-017-1226-y

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spelling	doaj-4c491a0bf7454936878310d83b4ce2522020-11-25T00:39:57ZengSpringerOpenAdvances in Difference Equations1687-18472017-06-01201711910.1186/s13662-017-1226-yExistence of solutions for a mixed fractional boundary value problemA Guezane Lakoud0R Khaldi1Adem Kılıçman2Laboratory of Advanced Materials, Department of Mathematics, Badji Mokhtar-Annaba UniversityLaboratory of Advanced Materials, Department of Mathematics, Badji Mokhtar-Annaba UniversityDepartment of Mathematics, Universiti Putra MalaysiaAbstract In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii’s fixed point theorem to conclude the existence of nontrivial solutions.http://link.springer.com/article/10.1186/s13662-017-1226-yboundary value problemfractional derivativefixed point theoremexistence of solutionintegral equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	A Guezane Lakoud R Khaldi Adem Kılıçman
spellingShingle	A Guezane Lakoud R Khaldi Adem Kılıçman Existence of solutions for a mixed fractional boundary value problem Advances in Difference Equations boundary value problem fractional derivative fixed point theorem existence of solution integral equation
author_facet	A Guezane Lakoud R Khaldi Adem Kılıçman
author_sort	A Guezane Lakoud
title	Existence of solutions for a mixed fractional boundary value problem
title_short	Existence of solutions for a mixed fractional boundary value problem
title_full	Existence of solutions for a mixed fractional boundary value problem
title_fullStr	Existence of solutions for a mixed fractional boundary value problem
title_full_unstemmed	Existence of solutions for a mixed fractional boundary value problem
title_sort	existence of solutions for a mixed fractional boundary value problem
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2017-06-01
description	Abstract In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii’s fixed point theorem to conclude the existence of nontrivial solutions.
topic	boundary value problem fractional derivative fixed point theorem existence of solution integral equation
url	http://link.springer.com/article/10.1186/s13662-017-1226-y
work_keys_str_mv	AT aguezanelakoud existenceofsolutionsforamixedfractionalboundaryvalueproblem AT rkhaldi existenceofsolutionsforamixedfractionalboundaryvalueproblem AT ademkılıcman existenceofsolutionsforamixedfractionalboundaryvalueproblem
_version_	1725292237434126336

Existence of solutions for a mixed fractional boundary value problem

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