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Entropy 2016, 18(11), 420; doi:10.3390/e18110420

On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations

1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416, Iran
2
Department of Mathematical Sciences, University of South Africa (UNISA), Pretoria 0003, South Africa
3
Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah 64001, Iraq
4
Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
5
Department of Mathematics, Çankaya University, Ankara 06530, Turkey
6
Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest RO-76911, Romania
*
Author to whom correspondence should be addressed.
Academic Editors: Carlo Cattani and Kevin H. Knuth
Received: 21 June 2016 / Revised: 26 October 2016 / Accepted: 21 November 2016 / Published: 23 November 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
View Full-Text   |   Download PDF [229 KB, uploaded 24 November 2016]

Abstract

In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results. View Full-Text
Keywords: existence and uniqueness solutions; local fractional differential equations; contracting mapping theorem; local fractional operators existence and uniqueness solutions; local fractional differential equations; contracting mapping theorem; local fractional operators
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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Jafari, H.; Jassim, H.K.; Al Qurashi, M.; Baleanu, D. On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations. Entropy 2016, 18, 420.

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