Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions

In this paper, we establish the existence and uniqueness of solution for a class of boundary value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder's fixed point theorem and the non...

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Main Authors:	Mouffak Benchohra, Jamal E. Lazreg
Format:	Article
Language:	English
Published:	Conspress 2014-05-01
Series:	Romanian Journal of Mathematics and Computer Science
Subjects:	Boundary value problem Caputo's fractional derivative implicit fractional dierential equations fractional integral existence Green's function Gronwall's lemma xed point fixed point
Online Access:	http://www.rjm-cs.ro/BenchohraRazreg-2014.pdf

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spelling	doaj-83f7268ee57d477e9fa935b35bb5661a2020-11-24T22:12:39ZengConspressRomanian Journal of Mathematics and Computer Science2247-689X2014-05-01416072Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary ConditionsMouffak Benchohra0Jamal E. Lazreg1Laboratory of Mathematics, University of Sidi Bel-Abbes, P. O. Box 89, Sidi Bel-Abbes 22000, Algeria, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, e-mail: benchohra@yahoo.comLaboratory of Mathematics, University of Sidi Bel-Abbes, P. O. Box 89, Sidi Bel-Abbes 22000, Algeria, e-mail:lazregjamal@yahoo.frIn this paper, we establish the existence and uniqueness of solution for a class of boundary value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder's fixed point theorem and the nonlinear alterna- tive of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.http://www.rjm-cs.ro/BenchohraRazreg-2014.pdfBoundary value problemCaputo's fractional derivativeimplicit fractional dierential equationsfractional integralexistenceGreen's functionGronwall's lemmaxed pointfixed point
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mouffak Benchohra Jamal E. Lazreg
spellingShingle	Mouffak Benchohra Jamal E. Lazreg Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions Romanian Journal of Mathematics and Computer Science Boundary value problem Caputo's fractional derivative implicit fractional dierential equations fractional integral existence Green's function Gronwall's lemma xed point fixed point
author_facet	Mouffak Benchohra Jamal E. Lazreg
author_sort	Mouffak Benchohra
title	Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions
title_short	Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions
title_full	Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions
title_fullStr	Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions
title_full_unstemmed	Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions
title_sort	existence and uniqueness results for nonlinear implicit fractional differential equations with boundary conditions
publisher	Conspress
series	Romanian Journal of Mathematics and Computer Science
issn	2247-689X
publishDate	2014-05-01
description	In this paper, we establish the existence and uniqueness of solution for a class of boundary value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder's fixed point theorem and the nonlinear alterna- tive of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.
topic	Boundary value problem Caputo's fractional derivative implicit fractional dierential equations fractional integral existence Green's function Gronwall's lemma xed point fixed point
url	http://www.rjm-cs.ro/BenchohraRazreg-2014.pdf
work_keys_str_mv	AT mouffakbenchohra existenceanduniquenessresultsfornonlinearimplicitfractionaldifferentialequationswithboundaryconditions AT jamalelazreg existenceanduniquenessresultsfornonlinearimplicitfractionaldifferentialequationswithboundaryconditions
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Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions

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