Browsing by Author "Senu, Norazak"

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Citation Count: Salahshour, S...et al. (2015). A new fractional derivative for differential equation of fractional order under interval uncertainty. Advance In Mechanical Engineering, 7(12). http://dx.doi.org/10.1177/1687814015619138
A new fractional derivative for differential equation of fractional order under interval uncertainty
(Sage Publications LTD, 2015) Salahshour, Soheil; Ahmadian, Ali; Ismail, Fudziah; 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
Citation Count: Salahshour, S...et al. (2015). On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem. Entropy, 17(2), 885-902. http://dx.doi.org/10.3390/e17020885
On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem
(MDPI AG, 2015) Salahshour, Soheil; Ahmadian, Ali; Senu, Norazak; Baleanu, Dumitru; Agarwal, Ravi P.
In this paper, we apply the concept of Caputo's H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann-Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
Citation Count: Salahshour, Soheil; Ahmadian...et al. (2019). "Uncertain Fractional Operator With Application Arising in the Steady Heat Flow", Vol. 23, No. 2, pp. 1289-1296.
Uncertain Fractional Operator With Application Arising in the Steady Heat Flow
(Vinca Inst Nuclear Sci, 2019) Salahshour, Soheil; Ahmadian, Ali; Ali-Akbari, Mahdi; Senu, Norazak; Baleanu, Dumitru; 56389
In the recent years much efforts were made to propose simple and well-behaved fractional operators to inherit the classical properties from the first order derivative and overcome the singularity problem of the kernel appearing for the existing fractional derivatives. Therefore, we propose in this research an interesting approach to acquire the interval solution of fractional interval differential equations under a new fractional operator, that does not have the above defect with uncertain parameters. In fact, this scheme is developed to achieve the interval solution of the uncertain steady heat flow based on the fractional interval differential equations. An example is experienced to illustrate our approach and validate it.