Implicit Fractional Differential Equations via the Liouville–Caputo Derivative

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.

Bibliographic Details
Main Authors:	Juan J. Nieto, Abelghani Ouahab, Venktesh Venktesh
Format:	Article
Language:	English
Published:	MDPI AG 2015-05-01
Series:	Mathematics
Subjects:	fractional differential equations fractional integral fractional derivative Liouville–Caputo derivative implicit
Online Access:	http://www.mdpi.com/2227-7390/3/2/398

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spelling	doaj-b45aa0a2f7664ed7856fbd4c01d9f7e02020-11-24T21:05:13ZengMDPI AGMathematics2227-73902015-05-013239841110.3390/math3020398math3020398Implicit Fractional Differential Equations via the Liouville–Caputo DerivativeJuan J. Nieto0Abelghani Ouahab1Venktesh Venktesh2Department of Mathematical Analysis, University of Santiago de Compostela, Santiago de Compostela 15782, SpainLaboratory of Mathematics, Sidi-Bel-Abbès University, P.O. Box 89, Sidi-Bel-Abbès 22000, AlgeriaDepartment of Mathematical Analysis, University of Santiago de Compostela, Santiago de Compostela 15782, SpainWe study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.http://www.mdpi.com/2227-7390/3/2/398fractional differential equationsfractional integralfractional derivativeLiouville–Caputo derivativeimplicit
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Juan J. Nieto Abelghani Ouahab Venktesh Venktesh
spellingShingle	Juan J. Nieto Abelghani Ouahab Venktesh Venktesh Implicit Fractional Differential Equations via the Liouville–Caputo Derivative Mathematics fractional differential equations fractional integral fractional derivative Liouville–Caputo derivative implicit
author_facet	Juan J. Nieto Abelghani Ouahab Venktesh Venktesh
author_sort	Juan J. Nieto
title	Implicit Fractional Differential Equations via the Liouville–Caputo Derivative
title_short	Implicit Fractional Differential Equations via the Liouville–Caputo Derivative
title_full	Implicit Fractional Differential Equations via the Liouville–Caputo Derivative
title_fullStr	Implicit Fractional Differential Equations via the Liouville–Caputo Derivative
title_full_unstemmed	Implicit Fractional Differential Equations via the Liouville–Caputo Derivative
title_sort	implicit fractional differential equations via the liouville–caputo derivative
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2015-05-01
description	We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.
topic	fractional differential equations fractional integral fractional derivative Liouville–Caputo derivative implicit
url	http://www.mdpi.com/2227-7390/3/2/398
work_keys_str_mv	AT juanjnieto implicitfractionaldifferentialequationsviatheliouvillecaputoderivative AT abelghaniouahab implicitfractionaldifferentialequationsviatheliouvillecaputoderivative AT venkteshvenktesh implicitfractionaldifferentialequationsviatheliouvillecaputoderivative
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Implicit Fractional Differential Equations via the Liouville–Caputo Derivative

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