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.
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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 |
_version_ |
1716769556779761664 |