Browsing by Author "Abbasbandy, S."

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Citation Count: Salahshour, S...et al. (2012). "Existence and uniqueness results for fractional differential equations with uncertainty", Advances In Difference Equations.
Existence and Uniqueness Results for Fractional Differential Equations With Uncertainty
(Springer International Publishing AG, 2012) Salahshour, S.; Allahviranloo, Tofigh; Abbasbandy, S.; Baleanu, Dumitru; 56389
In this paper, we study the existence, uniqueness and approximate solutions of fuzzy fractional differential equations (FFDEs) under Caputo's H-differentiability. To this end, the concept of Riemann-Liouville's H-differentiability is introduced, and subsequently, the Caputo's H-differentiability is proposed. Moreover, the related fuzzy Volterra integral forms of FFDEs are obtained which are applied to construct two converge consequences of fuzzy-valued functions as approximated solutions of FFDEs.
Citation Count: Salahshour, S.; Ahmadian, A.; Abbasbandy, S.; et al., "M-fractional derivative under interval uncertainty: Theory, properties and applications", Chaos Solitons & Fractals, Vol. 117, pp. 84-93, (2018).
M-fractional derivative under interval uncertainty: Theory, properties and applications
(Pergamon-Elsevier Science LTD, 2018) Salahshour, S.; Ahmadian, Ali; Abbasbandy, S.; Baleanu, Dumitru; 56389
In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherit the classical properties from the first order derivative. In this regards, the truncated M-fractional derivative for alpha-differentiable function was recently introduced that is a generalization of four fractional derivatives presented in the literature and has their important features. In this research, we aim to generalize this novel and effective derivative under interval uncertainty. The concept of interval truncated M-fractional derivative is introduced and some of the distinguished properties of this interesting fractional derivative such as Rolle's and mean value theorems, are developed for the interval functions. In addition, the existence and uniqueness conditions of the solution for the interval fractional differential equations (IFDEs) based on this new derivative are also investigated. Finally, we present the applicability of this novel interval fractional derivative for IFDEs based on the notion of w-increasing (w-decreasing) by solving a number of test problems. (C) 2018 Elsevier Ltd. All rights reserved.
Citation Count: Allahviranloo, T...et al. (2013). "On Solutions of Linear Fractional Differential Equations with Uncertainty", Abstract and Applied Analysis.
On Solutions of Linear Fractional Differential Equations With Uncertainty
(Hindawi LTD, 2013) Allahviranloo, Tofigh; Abbasbandy, S.; Shahryari, M. R. Balooch; Salahshour, S.; Baleanu, Dumitru; 56389
The solutions of linear fuzzy fractional differential equations (FFDEs) under the Caputo differentiability have been investigated. To this end, the fuzzy Laplace transform was used to obtain the solutions of FFDEs. Then, some new results regarding the relation between some types of differentiability have been obtained. Finally, some applicable examples are solved in order to show the ability of the proposed method.