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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Hindawi Publishing Corporation
2016
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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 |
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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. |
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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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