$Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems$

Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems

We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to...

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Main Authors:	Choukri Derbazi, Hadda Hammouche
Format:	Article
Language:	English
Published:	Institute of Mathematics of the Czech Academy of Science 2021-10-01
Series:	Mathematica Bohemica
Subjects:	fractional langevin equation caputo fractional derivative integrable solution existence uniqueness initial value problem fixed point theorem
Online Access:	http://mb.math.cas.cz/full/146/3/mb146_3_9.pdf

id	doaj-9ae8de55289542c6a606ea9cf1cde108
record_format	Article
spelling	doaj-9ae8de55289542c6a606ea9cf1cde1082021-08-13T05:11:41ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362021-10-01146336337410.21136/MB.2020.0004-19MB.2020.0004-19Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problemsChoukri DerbaziHadda HammoucheWe study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.http://mb.math.cas.cz/full/146/3/mb146_3_9.pdf fractional langevin equation caputo fractional derivative integrable solution existence uniqueness initial value problem fixed point theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Choukri Derbazi Hadda Hammouche
spellingShingle	Choukri Derbazi Hadda Hammouche Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems Mathematica Bohemica fractional langevin equation caputo fractional derivative integrable solution existence uniqueness initial value problem fixed point theorem
author_facet	Choukri Derbazi Hadda Hammouche
author_sort	Choukri Derbazi
title	Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
title_short	Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
title_full	Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
title_fullStr	Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
title_full_unstemmed	Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
title_sort	existence and uniqueness of integrable solutions to fractional langevin equations involving two fractional orders with initial value problems
publisher	Institute of Mathematics of the Czech Academy of Science
series	Mathematica Bohemica
issn	0862-7959 2464-7136
publishDate	2021-10-01
description	We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.
topic	fractional langevin equation caputo fractional derivative integrable solution existence uniqueness initial value problem fixed point theorem
url	http://mb.math.cas.cz/full/146/3/mb146_3_9.pdf
work_keys_str_mv	AT choukriderbazi existenceanduniquenessofintegrablesolutionstofractionallangevinequationsinvolvingtwofractionalorderswithinitialvalueproblems AT haddahammouche existenceanduniquenessofintegrablesolutionstofractionallangevinequationsinvolvingtwofractionalorderswithinitialvalueproblems
_version_	1721209101809090560

Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems

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