Pub Date : 2023-01-26DOI: 10.11121/ijocta.2023.1178
Lavina Sahijwani, N. Sukavanam
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.
{"title":"Approximate controllability for systems of fractional nonlinear differential equations involving Riemann-Liouville derivatives","authors":"Lavina Sahijwani, N. Sukavanam","doi":"10.11121/ijocta.2023.1178","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1178","url":null,"abstract":"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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85456620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-26DOI: 10.11121/ijocta.2023.1218
Anal Chatterjee, Samares Pal
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.
{"title":"A predator-prey model for the optimal control of fish harvesting through the imposition of a tax","authors":"Anal Chatterjee, Samares Pal","doi":"10.11121/ijocta.2023.1218","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1218","url":null,"abstract":"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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85873741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-26DOI: 10.11121/ijocta.2023.1223
M. M. Özyetkin, Hasan Birdane
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.
{"title":"The processes with fractional order delay and PI controller design using particle swarm optimization","authors":"M. M. Özyetkin, Hasan Birdane","doi":"10.11121/ijocta.2023.1223","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1223","url":null,"abstract":"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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"110 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79265443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-24DOI: 10.11121/ijocta.2023.1265
N. S. Malagi, P. Veeresha, G. D. Prasanna, B. Prasannakumara, D. G. Prakasha
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 q-homotopy analysis method and the new integral transform known as Elzaki transform called, q-homotopy analysis Elzaki transform method (q-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. q-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 q-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.
{"title":"Novel approach for nonlinear time-fractional Sharma-Tasso-Olever equation using Elzaki transform","authors":"N. S. Malagi, P. Veeresha, G. D. Prasanna, B. Prasannakumara, D. G. Prakasha","doi":"10.11121/ijocta.2023.1265","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1265","url":null,"abstract":"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 q-homotopy analysis method and the new integral transform known as Elzaki transform called, q-homotopy analysis Elzaki transform method (q-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. q-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 q-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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"10 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72417973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-24DOI: 10.11121/ijocta.2023.1238
Gamze Sekeroglu, Kazım Karaboga
This study aims to determine the effects of R&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&D and marketing expenditures on stock return showed that the effect of R&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&D and marketing expenditures on return on assets and return on equity. The results implied a positive and significant relationship between R&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.
{"title":"The effect of marketing and R&D expenditures on firm profitability and stock return: Evidence from BIST","authors":"Gamze Sekeroglu, Kazım Karaboga","doi":"10.11121/ijocta.2023.1238","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1238","url":null,"abstract":"This study aims to determine the effects of R&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&D and marketing expenditures on stock return showed that the effect of R&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&D and marketing expenditures on return on assets and return on equity. The results implied a positive and significant relationship between R&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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"2016 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87797071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-23DOI: 10.11121/ijocta.2023.1243
M. T. Hoang, Thi Kim Quy Ngo, Ha Hai Truong
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.
{"title":"A simple method for studying asymptotic stability of discrete dynamical systems and its applications","authors":"M. T. Hoang, Thi Kim Quy Ngo, Ha Hai Truong","doi":"10.11121/ijocta.2023.1243","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1243","url":null,"abstract":"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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"27 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83260386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-23DOI: 10.11121/ijocta.2023.1072
Saida Zenfari, M. Laabissi, M. E. Achhab
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.
{"title":"Observer design for a class of irreversible port Hamiltonian systems","authors":"Saida Zenfari, M. Laabissi, M. E. Achhab","doi":"10.11121/ijocta.2023.1072","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1072","url":null,"abstract":"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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"300 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76268186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-23DOI: 10.11121/ijocta.2023.1258
S. Jain, Rahul Goyal, P. Agarwal, S. Momani
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.
{"title":"Certain saigo type fractional integral inequalities and their q-analogues","authors":"S. Jain, Rahul Goyal, P. Agarwal, S. Momani","doi":"10.11121/ijocta.2023.1258","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1258","url":null,"abstract":"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.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"2 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79426620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-29DOI: 10.11121/ijocta.2022.1219
Aisha Gokce, Burcu Gurbuz
Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tissue in mathematical neuroscience. Studying these models with a sigmoidal firing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectivities. Because of the convolution structure of these integrals, it is possible to evaluate neural field model using a pseudo-spectral method, where Fourier Transform (FT) followed by an inverse Fourier Transform (IFT) is performed, leading to a new identical partial differential equation. In this paper, we revisit a neural field model with a nonlinear sigmoidal firing rate and provide an efficient numerical algorithm to analyse the model regarding finite volume scheme. On the other hand, numerical results are obtained by the algorithm.
{"title":"A numerical scheme for the one-dimensional neural field model","authors":"Aisha Gokce, Burcu Gurbuz","doi":"10.11121/ijocta.2022.1219","DOIUrl":"https://doi.org/10.11121/ijocta.2022.1219","url":null,"abstract":"Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tissue in mathematical neuroscience. Studying these models with a sigmoidal firing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectivities. Because of the convolution structure of these integrals, it is possible to evaluate neural field model using a pseudo-spectral method, where Fourier Transform (FT) followed by an inverse Fourier Transform (IFT) is performed, leading to a new identical partial differential equation. In this paper, we revisit a neural field model with a nonlinear sigmoidal firing rate and provide an efficient numerical algorithm to analyse the model regarding finite volume scheme. On the other hand, numerical results are obtained by the algorithm.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79506018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-27DOI: 10.11121/ijocta.2022.1112
N. Taş, N. Özgür
In this paper, our aim is to obtain a new generalization of the well-known Rhoades' contractive condition. To do this, we introduce the notion of an S-normed space. We extend the Rhoades' contractive condition to S-normed spaces and define a new type of contractive conditions. We support our theoretical results with necessary illustrative examples.
{"title":"A new generalization of Rhoades' condition","authors":"N. Taş, N. Özgür","doi":"10.11121/ijocta.2022.1112","DOIUrl":"https://doi.org/10.11121/ijocta.2022.1112","url":null,"abstract":"In this paper, our aim is to obtain a new generalization of the well-known Rhoades' contractive condition. To do this, we introduce the notion of an S-normed space. We extend the Rhoades' contractive condition to S-normed spaces and define a new type of contractive conditions. We support our theoretical results with necessary illustrative examples.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"9 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78731042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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