Browsing by Author "Zafar, Zain Ul Abadin"

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Analysis and Numerical Simulation of Tuberculosis Model Using Different
(Pergamon-elsevier Science Ltd, 2022) Zafar, Zain Ul Abadin; Zaib, Sumera; Hussain, Muhammad Tanveer; Tunc, Cemil; Javeed, Shumaila
The main goal of the current research is to study and explore dynamic behavior of tuberculosis by using fractional mathematical model. In this study, recently introduced fractional operator (FO) having ML non-singular kernel was used. Fixed point theory is utilized to explore the unique and existing problems in suitable model. Numerical outcomes are discovered for the verification of arbitrary fractional order derivative. These numerical outcomes are discovered from mathematical and biological perspectives by using the model parameters values. Graphical simulation shows the comparison between Fractional Caputo (Fr. Cap) method and AB Caputo (AB Cap) predictor corrector method for different fraction order. The present study suggested that AB Cap is much better than Fr. Cap.(c) 2022 Elsevier Ltd. All rights reserved.
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/).
An Efficient Numerical Simulation and Mathematical Modeling for the Prevention of Tuberculosis
(World Scientific Publ Co Pte Ltd, 2022) Zafar, Zain Ul Abadin; Younas, Samina; Zaib, Sumera; Tunc, Cemil
The main purpose of this research is to use a fractional-mathematical model including Atangana-Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor-corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.
Fractional Aspects of Coupled Mass-Spring System
(Pergamon-elsevier Science Ltd, 2021) Zafar, Zain Ul Abadin; Younas, Samina; Hussain, Muhammad Tanveer; Tunc, Cemil
In this article, the non-integer equations of the coupled mass-spring system with Atangana Baleanu fractional derivatives is offered. The physical entities of the structure are well-preserved by presenting an supplementary stricture chi. A nonlinear model with damping factor is considered. The existence and uniqueness problem to related model are scanned by fixed point principle. Our consequences spectacle that the mechanical components reveal viscoelastic behaviors generating temporal fractality at diverse scales and exhibit the existence of material heterogeneities in the mechanical modules. The comparison Jajarmi predictor corrector and Caputo methods is also given. (C) 2021 Published by Elsevier Ltd.
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.
Numerical Analysis of Bazykin-Berezovskaya Model
(Taylor & Francis Ltd, 2023) Zafar, Zain Ul Abadin; Saeed, Syed Tauseef; Qureshi, Muhammad Rehan; Tunc, Cemil
In this manuscript, a Bazykin-Berezovskaya model with diffusion by strong Allee effects is studied. Neumann boundary conditions are used to see the positive solution of a diffusion system. Local stability analyses are discussed for all the equilibrium points. The analysis of stability for the proposed scheme is also given. Implicit finite difference schemes like: Euler, Crank-Nicolson (CN) and non-standard finite difference (NSFD) are used to verify the simulation by numerically. A comparison reveals that NSFD method is unconditionally stable for any temporal step-size.