A new fractional derivative for differential equation of fractional order under interval uncertainty

In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathemati...

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Main Authors: Salahshour, Soheil, Ahmadian, Ali, Ismail, Fudzial, Baleanu, Dumitru, Senu, Norazak
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2016
Online Access:http://psasir.upm.edu.my/id/eprint/54873/1/A%20New%20fractional%20derivative%20for%20differential%20equation%20of%20fractional%20order.pdf
http://psasir.upm.edu.my/id/eprint/54873/
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Institution: Universiti Putra Malaysia
Language: English
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spelling my.upm.eprints.548732018-06-12T02:16:14Z http://psasir.upm.edu.my/id/eprint/54873/ A new fractional derivative for differential equation of fractional order under interval uncertainty Salahshour, Soheil Ahmadian, Ali Ismail, Fudzial Baleanu, Dumitru Senu, Norazak In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models. Hindawi Publishing Corporation 2016 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/54873/1/A%20New%20fractional%20derivative%20for%20differential%20equation%20of%20fractional%20order.pdf Salahshour, Soheil and Ahmadian, Ali and Ismail, Fudzial and Baleanu, Dumitru and Senu, Norazak (2016) A new fractional derivative for differential equation of fractional order under interval uncertainty. Advances in Mechanical Engineering, 7 (12). pp. 1-11. ISSN 1687-8132; ESSN: 1687-8140 10.1177/1687814015619138
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models.
format Article
author Salahshour, Soheil
Ahmadian, Ali
Ismail, Fudzial
Baleanu, Dumitru
Senu, Norazak
spellingShingle Salahshour, Soheil
Ahmadian, Ali
Ismail, Fudzial
Baleanu, Dumitru
Senu, Norazak
A new fractional derivative for differential equation of fractional order under interval uncertainty
author_facet Salahshour, Soheil
Ahmadian, Ali
Ismail, Fudzial
Baleanu, Dumitru
Senu, Norazak
author_sort Salahshour, Soheil
title A new fractional derivative for differential equation of fractional order under interval uncertainty
title_short A new fractional derivative for differential equation of fractional order under interval uncertainty
title_full A new fractional derivative for differential equation of fractional order under interval uncertainty
title_fullStr A new fractional derivative for differential equation of fractional order under interval uncertainty
title_full_unstemmed A new fractional derivative for differential equation of fractional order under interval uncertainty
title_sort new fractional derivative for differential equation of fractional order under interval uncertainty
publisher Hindawi Publishing Corporation
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/54873/1/A%20New%20fractional%20derivative%20for%20differential%20equation%20of%20fractional%20order.pdf
http://psasir.upm.edu.my/id/eprint/54873/
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