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Zahra Alijani

Bio: Zahra Alijani is an academic researcher from University of Tartu. The author has contributed to research in topics: Fuzzy logic & Collocation method. The author has an hindex of 5, co-authored 11 publications receiving 181 citations. Previous affiliations of Zahra Alijani include Institute for Advanced Studies in Basic Sciences.

Papers
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Journal ArticleDOI
TL;DR: New numeric methods based on the first and second degree F-transform for solving the Cauchy problem show that they outperform the second order RungeKutta method especially when a right-hand function is oscillating and/or a solution is requested on a long interval.

82 citations

Journal ArticleDOI
TL;DR: In this article, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application, and the superconvergent results on the graded mesh are studied.
Abstract: In this paper, systems of fuzzy fractional differential equations with a lateral type of the Hukuhara derivative and the generalized Hukuhara derivative are numerically studied. Collocation method on discontinuous piecewise polynomial spaces is proposed. Convergence of the proposed method is analyzed. The superconvergent results on the graded mesh are studied. Examples are provided to support theoretical results. Finally, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application.

76 citations

Journal ArticleDOI
TL;DR: In this article, a numerical method based on the fuzzy transform for solving second-order differential equations with boundary conditions is presented, and the method is shown to be effective in some examples.
Abstract: We present a numerical method based on the fuzzy transform for solving second-order differential equations with boundary conditions. We demonstrate the effectiveness of the method by some examples. Copyright © 2016 John Wiley & Sons, Ltd.

38 citations

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TL;DR: This work proposes to use Chebyshev polynomials due to their smoothness and reasonable behavior near boundaries to solve fuzzy Fredholm integral equations of the second kind with respect to fuzzy valued functions using the ordinary approximation technique.

24 citations

Journal ArticleDOI
TL;DR: Using a generalization of division for fuzzy numbers, the existence and global behavior of the fuzzy difference equation x n + 1 = A + B x n , n = 0, 1, . . . , where A and B are positive fuzzy numbers is studied.

15 citations


Cited by
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TL;DR: Numerical results show the impressive performance of the fractional operator on the dynamic behavior of the considered predator-prey model and the numerical method used in the article is one of the most efficient patterns in solving problems with fractional derivatives.
Abstract: In recent decades, studying the behavior of biological species has become one of the most fascinating areas of applied mathematics. The high importance of conservation of rare species in nature has prompted researchers in various fields to pay particular attention to this issue. Therefore, it is essential to develop mathematical models that examine the dynamics of their behavior. On the other hand, the development of new concepts in numerical analysis has enabled us to preserve more information on the evolutionary behavior history of a dynamic system and to use it in predicting the new features of the system. Fractional derivatives have provided such a valuable tool. This paper studies a dynamic system that models the interactions between two densities of immature and mature prey and predator populations. In the model, prey population is divided into two populations, including mature prey and immature prey. Another feature of the model is that predator depends on mature prey only and it followed by Crowley-Martin type functional response. Moreover, the fractional operator used in this model as derivative is of the Atangana-Baleanu AB type. Using this kind of fractional derivative causes the results to depend on the fractional order of the derivative. The addition of the concept of memory to the model is another highlight of using this type of derivative for the biological model. This helps the model to apply all the essential information of the phenomenon from the beginning to the desired time in the calculations. Existence and uniqueness of solutions to the fractional model are also investigated in this manuscript. The numerical method used in the article is also one of the most efficient patterns in solving problems with fractional derivatives. Using this effective method makes the results very consistent with what we actually expect to happen. Many simulations have been carried out to investigate the effect of parameters in the model on its overall behavior. Numerical results show the impressive performance of the fractional operator on the dynamic behavior of the considered predator-prey model. This efficient fractional operator can also be tested in the structure of other existing biological models.

68 citations

Journal ArticleDOI
TL;DR: In this article, a fuzzy Atangana-Baleanu-Caputo fractional derivative with uncertain constraints coefficients and initial conditions is introduced and analyzed, and a new computational algorithm is proposed to obtain analytic solutions of the studied equations.
Abstract: In this manuscript, we introduced, analyzed, and studied fuzzy fractional differential equations in terms of Atangana-Baleanu-Caputo differential operator equipped with uncertain constraints coefficients and initial conditions. To this end, we discussed both the fuzzy Atangana-Baleanu-Caputo fractional derivative and integral. Also, Newton-Leibniz fuzzy inversion formulas for both derivative and integral are proved. Using Banach fixed point theorem, existence and uniqueness results of solution are established by means of fuzzy strongly generalized differentiability of fuzzy fractional differential equation with Atangana-Baleanu fractional derivative under the Lipschitz condition. To achieve the above results, some prerequisite provisions for characterizing the solution in synonymous systems of crisp Atangana-Baleanu-Caputo fractional differential equations are argued. In this tendency, a new computational algorithm is proposed to obtain analytic solutions of the studied equations. To grasp the debated approach, some illustrative examples are provided and analyzed by the figures to visualize and support the theoretical results.

65 citations

Journal ArticleDOI
TL;DR: In this article, a class of tempered fractional differential equations with terminal value problems are investigated and Discretized collocation methods on piecewise polynomials spaces are proposed for solving these equations.

61 citations

Journal ArticleDOI
01 Sep 2020-Optik
TL;DR: In this paper, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application, and the superconvergent results on the graded mesh are studied.

55 citations