An International Journal of Optimization and Control: Theories & Applications (IJOCTA) http://ijocta.org/index.php/files <p> </p> <table> <tbody> <tr> <td width="230"> <p><img src="http://www.ijocta.org/public/site/images/fevirgen/ijoctakapak-606.jpg" alt="" width="212" height="300" /></p> <p><br />ISSN: 2146-0957<br />eISSN: 2146-5703</p> <p> </p> <p><strong>EDITOR IN CHIEF</strong> <br /><span style="color: #306754;"><a href="https://www.atlas.edu.tr/muhendislik-ve-doga-bilimleri-fakultesi-eski/prof-dr-ramazan-yaman/" target="_blank" rel="noopener">YAMAN, Ramazan</a> </span><br />Istanbul Atlas University / Turkey</p> <p><a href="http://ijocta.org/index.php/files/about/editorialTeam"><em>View the full editorial board</em></a></p> </td> <td> <p><strong>Aims and Scope</strong><br /><em>An International Journal of Optimization and Control: Theories &amp; Applications</em> is a scientific, peer-reviewed, open-access journal that publishes original research papers and review articles of high scientific value in all areas of applied mathematics, optimization and control. It aims to focus on multi/inter-disciplinary research into the development and analysis of new methods for the numerical solution of real-world applications in engineering and applied sciences. The basic fields of this journal cover mathematical modeling, computational methodologies and (meta)heuristic algorithms in optimization, control theory and their applications. Note that new methodologies for solving recent optimization problems in operations research must conduct a comprehensive computational study and/or case study to show their applicability and practical relevance.</p> <p><strong>Journal Topics</strong> <br />The topics covered in the journal are (not limited to): <br />Applied Mathematics, Financial Mathematics, Control Theory, Optimal Control, Fractional Calculus and Applications, Modeling of Bio-systems for Optimization and Control, Linear Programming, Nonlinear Programming, Stochastic Programming, Parametric Programming, Conic Programming, Discrete Programming, Dynamic Programming, Nonlinear Dynamics, Stochastic Differential Equations, Optimization with Artificial Intelligence, Operational Research in Life and Human Sciences, Heuristic and Metaheuristic Algorithms in Optimization, Applications Related to Optimization in Engineering.</p> <p> </p> <p> </p> </td> </tr> <tr> <td> </td> <td> </td> </tr> </tbody> </table> Ramazan YAMAN en-US An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 2146-0957 <p>Articles published in IJOCTA 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="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 IJOCTA, 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</li><li>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><p> <a href="http://creativecommons.org/licenses/by/4.0/" rel="license"><img src="https://i.creativecommons.org/l/by/4.0/88x31.png" alt="Creative Commons License" /></a> This work is licensed under a <a href="http://creativecommons.org/licenses/by/4.0/" rel="license" target="_blank">Creative Commons Attribution 4.0 International License</a>.</p> Certain saigo type fractional integral inequalities and their q-analogues http://ijocta.org/index.php/files/article/view/1258 <p>The main purpose of the present article is to introduce certain new Saigo fractional integral inequalities and their q-extensions. We also studied some special cases of these inequalities involving Riemann-Liouville and Erdelyi-Kober fractional integral operators.</p> Shilpi Jain Rahul Goyal Praveen Agarwal Shaher Momani Copyright (c) 2023 Shilpi Jain, Rahul Goyal, Praveen Agarwal, Shaher Momani http://creativecommons.org/licenses/by/4.0 2023-01-23 2023-01-23 13 1 1 9 10.11121/ijocta.2023.1258 A simple method for studying asymptotic stability of discrete dynamical systems and its applications http://ijocta.org/index.php/files/article/view/1243 <p>In this work, we introduce a simple method for investigating the asymptotic stability of discrete dynamical systems, which can be considered as an extension of the classical Lyapunov's indirect method. This method is constructed based on the classical Lyapunov's indirect method and the idea proposed by Ghaffari and Lasemi in a recent work. The new method can be applicable even when equilibia of dynamical systems are non-hyperbolic. Hence, in many cases, the classical Lyapunov's indirect method fails but the new one can be used simply. In addition, by combining the new stability method with the Mickens' methodology, we formulate some nonstandard finite difference (NSFD) methods which are able to preserve the asymptotic stability of some classes of differential equation models even when they have non-hyperbolic equilibrium points. As an important consequence, some well-known results on stability-preserving NSFD schemes for autonomous dynamical systems are improved and extended. Finally, a set of numerical examples are performed to illustrate and support the theoretical findings.</p> Manh Tuan Hoang Thi Kim Quy Ngo Ha Hai Truong Copyright (c) 2023 Manh Tuan Hoang, Thi Kim Quy Ngo, Ha Hai Truong http://creativecommons.org/licenses/by/4.0 2023-01-23 2023-01-23 13 1 10 25 10.11121/ijocta.2023.1243 Observer design for a class of irreversible port Hamiltonian systems http://ijocta.org/index.php/files/article/view/1072 <p>In this paper we address the state estimation problem of a particular class of irreversible port Hamiltonian systems (IPHS), which are assumed to be partially observed. Our main contribution consists to design an observer such that the augmented system (plant + observer) is strictly passive. Under some additional assumptions, a Lyapunov function is constructed to ensure the stability of the coupled system. Finally, the proposed methodology is applied to the gas piston system model. Some simulation results are also presented.</p> Saida Zenfari Mohamed Laabissi Mohammed Elarbi Achhab Copyright (c) 2023 Saida Zenfari, Mohamed Laabissi, Mohammed Elarbi Achhab http://creativecommons.org/licenses/by/4.0 2023-01-23 2023-01-23 13 1 26 34 10.11121/ijocta.2023.1072 The effect of marketing and R&D expenditures on firm profitability and stock return: Evidence from BIST http://ijocta.org/index.php/files/article/view/1238 <p>This study aims to determine the effects of R&amp;D and marketing expenditures of companies that force marketing and finance to act together on stock return, return on assets, and return on equity. To this end, the quarterly frequency data of nine companies that were continuously traded in the BIST Technology Index between March 2009 and December 2020 were examined with panel-data analysis. In line with the purpose of the research, analyzes were carried out in three different models. First of all, we determined which tests should be performed on the models based on the cross-sectional dependence, homogeneity/heterogeneity, and panel unit root test results obtained for the established models. The results of panel least squares test carried out to determine the effect of R&amp;D and marketing expenditures on stock return showed that the effect of R&amp;D expenditures on stock return was not statistically significant while marketing expenditures had a positive and significant effect on stock return. Analyzes should be continued with cointegration tests according to the characteristics of the two models established to determine the effect of R&amp;D and marketing expenditures on return on assets and return on equity. The results implied a positive and significant relationship between R&amp;D expenditures and return on both assets and equity. While no statistically significant relationship was found between marketing expenditures and return on assets, there was a positive and significant relationship between marketing expenditures and return on equity.</p> Gamze Sekeroglu Kazım Karaboga Copyright (c) 2023 Gamze Sekeroglu, Kaz?m Karaboga http://creativecommons.org/licenses/by/4.0 2023-01-24 2023-01-24 13 1 35 45 10.11121/ijocta.2023.1238 Novel approach for nonlinear time-fractional Sharma-Tasso-Olever equation using Elzaki transform http://ijocta.org/index.php/files/article/view/1265 <p>In this article, we demonstrated the study of the time-fractional nonlinear Sharma-Tasso-Olever (STO) equation with different initial conditions. The novel technique, which is the mixture of the <em>q</em>-homotopy analysis method and the new integral transform known as Elzaki transform called, <em>q</em>-homotopy analysis Elzaki transform method (<em>q</em>-HAETM) implemented to find the adequate approximated solution of the considered problems. The wave solutions of the STO equation play a vital role in the nonlinear wave model for coastal and harbor designs. The demonstration of the considered scheme is done by carrying out some examples of time-fractional STO equations with different initial approximations. <em>q</em>-HAETM offers us to modulate the range of convergence of the series solution using , called the auxiliary parameter or convergence control parameter. By performing appropriate numerical simulations, the effectiveness and reliability of the considered technique are validated. The implementation of the new integral transform called the Elzaki transform along with the reliable analytical technique called the <em>q</em>-homotopy analysis method to examine the time-fractional nonlinear STO equation displays the novelty of the presented work. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.</p> Naveen Sanju Malagi Pundikala Veeresha Gunderi Dhananjaya Prasanna Ballajja Chandrappa Prasannakumara Doddabhadrappla Gowda Prakasha Copyright (c) 2023 Naveen Sanju Malagi, Pundikala Veeresha, Gunderi Dhananjaya Prasanna, Ballajja Chandrappa Prasannakumara, Doddabhadrappla Gowda Prakasha http://creativecommons.org/licenses/by/4.0 2023-01-24 2023-01-24 13 1 46 58 10.11121/ijocta.2023.1265 Approximate controllability for systems of fractional nonlinear differential equations involving Riemann-Liouville derivatives http://ijocta.org/index.php/files/article/view/1178 <p>The article objectifies the approximate controllability of fractional nonlinear differential equations having Riemann-Liouville derivatives. First, the existence of solutions is deduced through fixed point approach and then approximate controllability is proved using Cauchy convergence through iterative and approximate techniques. The theory of semigroup together with probability density function has been utilized to reach the desired conclusions.</p> Lavina Sahijwani Nagarajan Sukavanam Copyright (c) 2023 Lavina Sahijwani, Nagarajan Sukavanam http://creativecommons.org/licenses/by/4.0 2023-01-26 2023-01-26 13 1 59 67 10.11121/ijocta.2023.1178 A predator-prey model for the optimal control of fish harvesting through the imposition of a tax http://ijocta.org/index.php/files/article/view/1218 <p>This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results.</p> Anal Chatterjee Samares Pal Copyright (c) 2023 Anal Chatterjee, Samares Pal http://creativecommons.org/licenses/by/4.0 2023-01-26 2023-01-26 13 1 68 80 10.11121/ijocta.2023.1218 The processes with fractional order delay and PI controller design using particle swarm optimization http://ijocta.org/index.php/files/article/view/1223 <p>In this study, the stability analysis of systems with fractional order delay is presented. Besides, PI controller design using particle swarm optimization (PSO) technique for such systems is also presented. The PSO algorithm is used to obtain the controller parameters within the stability region. As it is known that it is not possible to investigate the stability of systems with fractional order delay using analytical methods such as the Routh-Hurwitz criterion. Furthermore, stability analysis of such systems is quite difficult. In this study, for stability testing of such systems, an approximation method previously introduced in the literature by the corresponding author is used. In addition, the unit step responses have been examined to evaluate the systems' performances. It should be noted that examining unit step responses of systems having fractional-order delay is not possible due to the absence of analytical methods. One of the aims of this study is to overcome this deficiency by using the proposed approximation method. Besides, a solution to the question of which controller parameter values should be selected in the stability region, which provides the calculation of all stabilizing PI controllers, is proposed using the PSO algorithm.</p> Münevver Mine Özyetkin Hasan Birdane Copyright (c) 2023 Münevver Mine Özyetkin, Hasan Birdane http://creativecommons.org/licenses/by/4.0 2023-01-26 2023-01-26 13 1 81 91 10.11121/ijocta.2023.1223 Stability tests and solution estimates for non-linear differential equations http://ijocta.org/index.php/files/article/view/1251 <p>This article deals with certain systems of delay differential equations (DDEs) and a system of ordinary differential equations (ODEs). Here, five new theorems are proved on the fundamental properties of solutions of these systems. The results on the properties of solutions consist of sufficient conditions and they dealt with uniformly asymptotically stability (UAS), instability and integrability of solutions of unperturbed systems of DDEs, boundedness of solutions of a perturbed system of DDEs at infinity and exponentially stability (ES) of solutions of a system of nonlinear ODEs. Here, the techniques of proofs depend upon the Lyapunov- Krasovski? functional (LKF) method and Lyapunov function (LF) method. For illustrations, in particular cases, four examples are constructed as applications. Some results of this paper are given at first time in the literature, and the other results generalize and improve some related ones in the literature.</p> Osman Tunç Copyright (c) 2023 Osman Tunç http://creativecommons.org/licenses/by/4.0 2023-01-29 2023-01-29 13 1 92 103 10.11121/ijocta.2023.1251 Analysing the market for digital payments in India using the predator-prey mode http://ijocta.org/index.php/files/article/view/1306 <p>Technology has revolutionized the way transactions are carried out in economies across the world. India too has witnessed the introduction of numerous modes of electronic payment in the past couple of decades, including e-banking services, National Electronic Fund Transfer (NEFT), Real Time Gross Settlement (RTGS) and most recently the Unified Payments Interface (UPI). While other payment mechanisms have witnessed a gradual and consistent increase in the volume of transactions, UPI has witnessed an exponential increase in usage and is almost on par with pre-existing technologies in the volume of transactions. This study aims to employ a modified Lotka-Volterra (LV) equations (also known as the Predator-Prey Model) to study the competition among different payment mechanisms. The market share of each platform is estimated using the LV equations and combined with the estimates of the total market size obtained using the Auto-Regressive Integrated Moving Average (ARIMA) technique. The result of the model predicts that UPI will eventually overtake the conventional digital payment mechanism in terms of market share as well as volume. Thus, the model indicates a scenario where both payment mechanisms would coexist with UPI being the dominant (or more preferred) mode of payment.</p> Vijith Raghavendra Pundikala Veeresha Copyright (c) 2023 Vijith Raghavendra , Pundikala Veeresha http://creativecommons.org/licenses/by/4.0 2023-01-29 2023-01-29 13 1 104 115 10.11121/ijocta.2023.1306 The null boundary controllability for the Mullins equation with periodic boundary conditions http://ijocta.org/index.php/files/article/view/1283 <p>In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system. After showing the existence and uniqueness of the solution of the adjoint system, we determine the admissible initial data class since the system is not always controllable under these boundary conditions. Finally, using this spectral analysis, we reduce the null controllability problem to the moment problem and solve the problem on this admissible initial class.</p> Isil Oner Copyright (c) 2023 Isil Oner http://creativecommons.org/licenses/by/4.0 2023-01-29 2023-01-29 13 1 116 122 10.11121/ijocta.2023.1283 M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation http://ijocta.org/index.php/files/article/view/1321 <p>This article aims to examine M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation (FE), which is a generalization of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations. The fractional (4+1)$-dimensional Fokas equation with the M-truncated derivatives is also studied first time in this study. The generalized projective Riccati equations method (GPREM) is successfully implemented. In the application of the presented method, a suitable fractional wave transformation is chosen to convert the proposed model into a nonlinear ordinary differential equation. Then, a linear equation system is acquired utilizing the GPREM, the system is solved, and the suitable solution sets are obtained. Dark and singular soliton solutions are successfully derived. Under the selection of appropriate values of the parameters, 2D, 3D, and contour plots are also displayed for some solutions.</p> Neslihan Ozdemir Copyright (c) 2023 Neslihan Ozdemir http://creativecommons.org/licenses/by/4.0 2023-01-29 2023-01-29 13 1 123 129 10.11121/ijocta.2023.1321 A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations http://ijocta.org/index.php/files/article/view/1256 <p>The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper. We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system. The application of well-known fixed point theorem methodologies is avoided in this paper. Finally, a fractional heat equation is discussed as an example.</p> Ritika Pandey Chandan Shukla Anurag Shukla Ashwini Upadhyay Arun Kumar Singh Copyright (c) 2023 Ritika Pandey, Chandan Shukla, Anurag Shukla, Ashwini Upadhyay, Arun Kumar Singh http://creativecommons.org/licenses/by/4.0 2023-01-31 2023-01-31 13 1 130 138 10.11121/ijocta.2023.1256