Mathematical Modelling and Numerical Simulation with Applications <h2>About the Journal</h2> <table cellspacing="10" cellpadding="10"> <tbody> <tr> <td valign="top" width="250"><img src="" 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=";hl=en" target="_blank" rel="noopener">Mehmet Yavuz</a>, PhD, Necmettin Erbakan University, Turkey</p> <p><strong><a href="" target="_blank" rel="noopener"><em>View the Full Editorial Board</em></a></strong></p> <h3>Technical Editor</h3> <a title="Dr." href="" target="_blank" rel="noopener">Halil İbrahim Özer</a> - Necmettin Erbakan University, Turkey <h3>English Editor</h3> <p><a title="Technical Editor of MMNSA" href="" target="_blank" rel="noopener">Abdulkadir Ünal </a> - Alanya Alaaddin Keykubat University, Turkey</p> <h3>Editorial Secretariat</h3> <p><a title="Editorial Secretariat" href=";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=";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. 1 (2022, March): 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> en-US <p>Articles published in <em>MMNSA</em> are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (<a href="">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 <em>MMNSA</em>, 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> (Mehmet Yavuz) (Halil İbrahim Özer) Sat, 22 Jan 2022 13:09:05 +0000 OJS 60 Ion temperature gradient modes driven soliton and shock by reduction perturbation method for electron-ion magneto-plasma <p>In our observation, we have used an easy and reliable approach of the reduction perturbation method to obtain the solution of the ion temperature gradient mode driven linear and nonlinear structures of relatively small amplitude. One can use that methodology in the more complex environment of the plasma and can obtain a straightforward approach toward his studies. We have studied different parameter impacts on the linear and nonlinear modes of the ITG by using data from tokamak plasma. Hence, our study is related to the tokamak plasma and one that can apply to the nonlinear electrostatic study of stiller and interstellar regimes where such types of plasma environment occur.</p> Aziz Khan, Abbas Khan, Muhammad Sinan Copyright (c) 2022 Aziz Khan, Abbas Khan, Muhammad Sinan Sat, 22 Jan 2022 00:00:00 +0000 Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms <p>In this paper, we consider the constructive equations of the fractional second-grade fluid. The considered fluid model is described by the Caputo derivative. The problem consists to determine the exact analytical solution using the Laplace transform method. The influence of the order of the used fractional operator has been presented in this paper. We also analyze the influence of the Prandtl number in the dynamics of the temperature distribution according to the variation of the order of the Caputo derivative. The impact of the second-grade parameter and the Grashof number in the dynamics of the velocity has been presented and discussed. The influences of the parameters used in the modeling have been interpreted in terms of a fractional context. In general, it is shown that the order of the fractional operator influences the diffusivity of the considered fluid. This influence can cause an increase or decrease in the temperature and velocity distributions. The main findings of the paper have been illustrated using the graphical representations of the considered distributions according to the order of the fractional operator.</p> Ndolane Sene Copyright (c) 2022 Ndolane Sene Wed, 26 Jan 2022 00:00:00 +0000 Bi-dimensional crime model based on anomalous diffusion with law enforcement effect <p>Several models based on discrete and continuous fields have been proposed to comprehend residential criminal dynamics. This study introduces a two-dimensional model to describe residential burglaries diffusion, employing Lèvy flights dynamics. A continuous model is presented, introducing bidimensional fractional operator diffusion and its differences with the 1-dimensional case. Our results show, graphically, the hotspot's existence solution in a 2-dimensional attractiveness field, even fractional derivative order is modified. We also provide qualitative evidence that steady-state approximation in one dimension by series expansion is insufficient to capture similar original system behavior. At least for the case where series coefficients have a linear relationship with derivative order. Our results show, graphically, the hotspot's existence solution in a 2-dimensional attractiveness field, even if fractional derivative order is modified. Two dynamic regimes emerge in maximum and total attractiveness magnitude as a result of fractional derivative changes, these regimes can be understood as considerations about different urban environments. Finally, we add a Law enforcement component, embodying the "Cops on dots" strategy; in the Laplacian diffusion dynamic, global attractiveness levels are significantly reduced by Cops on dots policy but lose efficacy in Lèvy flight-based diffusion regimen. The four-step Preditor-Corrector method is used for numerical integration, and the fractional operator is approximated, getting the advantage of the spectral methods to approximate spatial derivatives in two dimensions.</p> Francisco Javier Martínez-Farías, Anahí Alvarado-Sánchez, Eduardo Rangel-Cortes, Arturo Hernández-Hernández Copyright (c) 2022 Francisco Javier Martínez-Farías, Anahí Alvarado-Sánchez, Eduardo Rangel-Cortes, Arturo Hernández-Hernández Thu, 27 Jan 2022 00:00:00 +0000 Three-dimensional fractional system with the stability condition and chaos control <p>A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.</p> Molood Gholami, Reza Khoshsiar Ghaziani, Zohreh Eskandari Copyright (c) 2022 Molood Gholami, Reza Khoshsiar Ghaziani, Zohreh Eskandari Wed, 16 Feb 2022 00:00:00 +0000 Shock absorber system dynamic model in model-based environment <p>This paper addresses the mathematical modelling of aircraft landing gear based on the shock absorber system’s dynamics and examination of results depending on different touchdown scenarios and design parameters. The proposed methodology relies on determining an analytical formulation of the shock absorber system’s equation of motion, modelling this formulation on the model-based environment (Matlab/Simulink), and integrating with an accurate aircraft nonlinear dynamic model to observe the performance of landing gear in different touchdown or impact velocities. A suitable landing performance depends on different parameters which are related to the shock absorber system’s working principle. There are three subsystems of the main system which are hydraulic, pneumatic, and tire systems. Subsystems create a different sort of forces and behaviors. The air in the pneumatic system is compressed by the impact effect so it behaves like a spring and creates pneumatic or air spring force so the most effective parameter in this structure is determined as initial air volume. Hydraulic oil in the receptacle of the hydraulic system flow in an orifice hole when impact occurs so it behaves as a damper and creates damping or hydraulic force. The same working principle is acceptable for the air in the tire. The relationship between tire and ground creates a friction force based on dynamic friction coefficient depending on aircraft dynamics. As a result of this study effect of the impact velocity and initial air volume parameters on the system are examined and determined by optimization according to maximum initial load limits of aircraft and displacement of strut and tire surface.</p> Nafi Kulaksiz, Sevval Cip, Zeynep Gedikoglu, Muhsin Hancer Copyright (c) 2022 Nafi Kulaksiz, Sevval Cip, Zeynep Gedikoglu, Muhsin Hancer Thu, 31 Mar 2022 00:00:00 +0000