Mathematical Modelling and Numerical Simulation with Applications https://mmnsa.org/index.php/mmnsa <h2>About the Journal</h2> <table cellspacing="10" cellpadding="10"> <tbody> <tr> <td valign="top" width="250"><img src="http://mmnsa.org/docs/anasayfa7.png" alt="" width="150" height="150" /><br /> <h3>ISSN Online: 2791-8564</h3> <p> </p> <div> <div> <div> <h2>EDITOR-IN-CHIEF<span style="font-size: 0.875rem;"> </span></h2> </div> </div> <p><a title="Editor in Chief" href="https://scholar.google.com.tr/citations?user=ILxNgXgAAAAJ&amp;hl=en" target="_blank" rel="noopener">Mehmet Yavuz</a>, PhD, Necmettin Erbakan University, Turkey</p> <p><strong><a href="https://mmnsa.org/index.php/mmnsa/about/editorialteam" target="_blank" rel="noopener"><em>View the Full Editorial Board</em></a></strong></p> <h3>Technical Editor</h3> <a title="Dr." href="http://www.hiozer.com/" target="_blank" rel="noopener">Halil İbrahim Özer</a> - Necmettin Erbakan University, Turkey <h3>English Editor</h3> <p><a title="Technical Editor of MMNSA" href="http://abis.alanya.edu.tr/?psno=0424" target="_blank" rel="noopener">Abdulkadir Ünal </a> - Alanya Alaaddin Keykubat University, Turkey</p> <h3>Editorial Secretariat</h3> <p><a title="Editorial Secretariat" href="https://scholar.google.com/citations?hl=tr&amp;view_op=list_works&amp;gmla=AJsN-F7CFAvwgtjwffHndGF30cy9pdKoosfnlCDjj1iuirxc2S9vNOnAlDxBq4D_bFZUbDl7tXXgYUt6Vc67fMmXmmyjhNqKz4aIVVP_YKC4Veb1rve8AwU&amp;user=5_-GcBcAAAAJ" target="_blank" rel="noopener">Fatma Özlem Coşar</a>, Necmettin Erbakan University, Turkey</p> <p><a title="Editorial Secretariat" href="https://scholar.google.com.tr/citations?hl=en&amp;user=6Z-kr5wAAAAJ" target="_blank" rel="noopener">Müzeyyen Akman</a>, Necmettin Erbakan University, Turkey</p> <p> </p> <p><br /> </p> </div> </td> <td valign="top"> <h3>Aims and Scope</h3> <p style="text-align: justify;">The <strong><em>Mathematical Modelling and Numerical Simulation with Applications (MMNSA)</em></strong> is an international research journal, which publishes <strong>top-level original</strong> and review papers, short communications and proceedings on mathematical modelling in biology, engineering, medicine, chemistry, physics, and other areas. <strong><em>MMNSA</em></strong> focuses on research related to the <strong>mathematical modelling</strong> of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves <strong>interdisciplinary processes</strong>, and contributions in this area with <strong>numerical simulations</strong> are also encouraged. The scope of the journal is devoted to mathematical modelling with sufficiently advanced models, and the works studying mainly the existence and stability of stationary points of ODE systems without applications are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to <strong>real-world problems</strong>. The journal is essentially functioning on the basis of topical issues representing active areas of research. The authors are invited to submit papers to the announced issues or to suggest new issues.<br />Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.</p> <h3>Journal Topics</h3> <p style="text-align: justify;">Mathematical Modelling, Applied Mathematics, Financial Mathematics, Control Theory, Modeling of Real-World Problems, Numerical Simulation, Fractional Calculus and Applications, Modeling of Bio-systems for Optimization and Control, Control Theory and Fuzzy Theory with Applications, Linear Programming, Nonlinear Programming, Stochastic Programming, Dynamic Programming, Nonlinear Dynamics, Stochastic Differential Equations, Operational Research in Life and Human Sciences, Applications Related to Control on Engineering.</p> <p> </p> <h3>Current Issue</h3> <div class="current_issue_title">Vol. 2 No. 3 (2022, September): MMNSA</div> <div class="obj_issue_toc"> <div class="heading"> <div class="description"> <h3><br />In Progress</h3> <p style="text-align: justify;">This issue contains final, fully citable articles that are published online immediately after completing the review process with the volume/issue and an assigned DOI number.</p> </div> </div> </div> </td> </tr> </tbody> </table> <p> </p> Mehmet Yavuz en-US Mathematical Modelling and Numerical Simulation with Applications 2791-8564 <p>Articles published in <strong>MMNSA</strong> are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the <em>Creative Commons Attribution 4.0 International License</em> (<a href="https://creativecommons.org/licenses/by/4.0/legalcode">click here</a> to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.</p> <p>Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in <strong>MMNSA</strong>, so long as the original authors and source are credited.</p> <p><strong>The readers are free to:</strong></p> <ul> <li><strong>Share</strong> — copy and redistribute the material in any medium or format</li> <li><strong>Adapt</strong> — remix, transform, and build upon the material for any purpose, even commercially.</li> <li>The licensor cannot revoke these freedoms as long as you follow the license terms.</li> </ul> <p><strong>under the following terms:</strong></p> <ul> <li><strong>Attribution</strong> — You must give <strong>appropriate credit</strong>, provide a link to the license, and <strong>indicate if changes were made</strong>. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.</li> </ul> <ul> <li><strong>No additional restrictions</strong> — You may not apply legal terms or <strong>technological measures</strong> that legally restrict others from doing anything the license permits.</li> </ul> An efficient application of scrambled response approach to estimate the population mean of the sensitive variables https://mmnsa.org/index.php/mmnsa/article/view/31 <p>In the presence of one auxiliary variable and two auxiliary variables, we analyze various exponential estimators. The ranks of the auxiliary variables are also connected with the study variables, and there is a linkage between the study variables and the auxiliary variables. These ranks can be used to improve an estimator's accuracy. The Optional Randomized Response Technique (ORRT) and the Quantitative Randomized Response Technique are two techniques we utilize to estimate the sensitive variables from the population mean (QRRT). We used the scrambled response technique and checked the proposed estimators up to the first-order of approximation. The mean square error (MSE) equations are obtained for all the proposed ratio exponential estimators and show that our proposed exponential type estimator is more efficient than ratio estimators. The expression of mean square error is obtained up to the first degree of approximation. The empirical and theoretical comparison of the proposed estimators with existing estimators is also be carried out. We have shown that the proposed optional randomized response technique and quantitative randomized response model are always better than existing estimators. The simulation study is also carried out to determine the performance of the estimators. Few real-life data sets are also be applied in support of proposed estimators. It is observed that our suggested estimator is more efficient as compared to an existing estimator.</p> Atiqa Zahid Saadia Masood Sumaira Mubarik Anwarud Din Copyright (c) 2022 Atiqa Zahid, Saadia Masood, Sumaira Mubarik, Anwarud Din https://creativecommons.org/licenses/by/4.0 2022-08-10 2022-08-10 2 3 127 146 10.53391/mmnsa.2022.011 The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity https://mmnsa.org/index.php/mmnsa/article/view/38 <p>This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The <span dir="ltr" role="presentation">φ^</span><span dir="ltr" role="presentation">6</span>-model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.</p> Muhammad Abubakar Isah Asıf Yokuş Copyright (c) 2022 Muhammad Abubakar Isah, Asıf Yokuş https://creativecommons.org/licenses/by/4.0 2022-09-16 2022-09-16 2 3 147 163 10.53391/mmnsa.2022.012 Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption https://mmnsa.org/index.php/mmnsa/article/view/39 <p>This article deals with a Caputo fractional-order viral model that incorporates the non-cytolytic immune hypothesis and the mechanism of viral replication inhibition. Firstly, we establish the existence, uniqueness, non-negativity, and boundedness of the solutions of the proposed viral model. Then, we point out that our model has the following three equilibrium points: equilibrium point without virus, equilibrium state without immune system, and equilibrium point activated by immunity with humoral feedback. By presenting two critical quantities, the asymptotic stability of all said steady points is examined. Finally, we examine the finesse of our results by highlighting the impact of fractional derivatives on the stability of the corresponding steady points.</p> Mouhcine Naim Yassine Sabbar Anwar Zeb Copyright (c) 2022 Mouhcine Naim, Yassine Sabbar, Anwar Zeb https://creativecommons.org/licenses/by/4.0 2022-09-25 2022-09-25 2 3 164 176 10.53391/mmnsa.2022.013