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Browsing by Author "Ali, Nigar"

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    Article
    Analysis and Numerical Simulations of Fractional Order Vallis System
    (Elsevier, 2020) Zafar, Zain Ul Abadin; Ali, Nigar; Zaman, Gul; Thounthong, Phatiphat; Tunc, Cemil
    This paper represents a non-integer-order Vallis systems in which we applied the Gru & uml; nwald-Letnikov tactics with Binomial coefficients in order to realize the numerical simulations to a set of equations. Recently researchers reported in the literature that it is the generalization of integer order dynamical model. Several cases involving non-integer and integer analysis with differ-ent values of non-integer order have been applied to Vallis systems to see the behavior of simula-tions. To visualize the effect of non-integer order approach, the time histories and phase portraits have been plotted. The consequences expose that the non-integer-order Vallis model can reveal a genuine equitable comportment to Vallis systems and might bid greater perceptions towards the understanding of such complex dynamic systems (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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    Article
    Mathematical Modeling and Analysis of Fractional-Order Brushless Dc Motor
    (Springer, 2021) Zafar, Zain Ul Abadin; Ali, Nigar; Tunc, Cemil
    In this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville-Caputo noninteger derivative with the Mittag-Lefler kernel. We find that the fractional-order brushless DC motor system exhibits the character of chaos. For the proposed system, we show the largest exponent to be 0.711625. We calculate the equilibrium points of the model and discuss their local stability. We apply an iterative scheme by using the Laplace transform to find a special solution in this case. By taking into account the rule of trapezoidal product integration we develop two iterative methods to find an approximate solution of the system. We also study the existence and uniqueness of solutions. We take into account the numerical solutions for Caputo Liouville product integration and Atangana-Baleanu Caputo product integration. This scheme has an implicit structure. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results.