Journal
ADVANCES IN MECHANICAL ENGINEERING
Volume 7, Issue 12, Pages -Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1687814015619138
Keywords
Interval arithmetic; fractional derivative; interval-valued function; generalized Hukuhara differentiability; viscoelastic models
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Funding
- Ministry of Higher Education (MOHE), Malaysia under FRGS
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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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