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Mathematics 2015, 3(2), 398-411; doi:10.3390/math3020398

Implicit Fractional Differential Equations via the Liouville–Caputo Derivative

1
Department of Mathematical Analysis, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
2
Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3
Laboratory of Mathematics, Sidi-Bel-Abbès University, P.O. Box 89, Sidi-Bel-Abbès 22000, Algeria
4
Birla Institute of Technology & Science, Pilani 333031, India
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 16 March 2015 / Accepted: 13 May 2015 / Published: 25 May 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
View Full-Text   |   Download PDF [227 KB, uploaded 25 May 2015]

Abstract

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. View Full-Text
Keywords: fractional differential equations; fractional integral; fractional derivative;Liouville–Caputo derivative; implicit fractional differential equations; fractional integral; fractional derivative;Liouville–Caputo derivative; implicit
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Nieto, J.J.; Ouahab, A.; Venktesh, V. Implicit Fractional Differential Equations via the Liouville–Caputo Derivative. Mathematics 2015, 3, 398-411.

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