S. Bhatter, Sangeeta Kumawat, Bhamini Bhatia, S. Purohit
This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.
{"title":"Analysis of COVID-19 epidemic with intervention impacts by a fractional operator","authors":"S. Bhatter, Sangeeta Kumawat, Bhamini Bhatia, S. Purohit","doi":"10.11121/ijocta.1515","DOIUrl":"https://doi.org/10.11121/ijocta.1515","url":null,"abstract":"This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"23 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141808773","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}
Rafel Ibrahim Salih, S. Jawad, K. Dehingia, Anusmita Das
Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how chemotherapy and anxiety work together to affect the speed at which cancer cells multiply and the immune system’s response model is necessary to come up with ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological scare and chemotherapy on the interaction of cancer and immunity. The proposed model is accurately described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish three equilibrium positions. The stability analysis reveals that all equilibrium points consistently exhibit stability under the defined conditions. The bifurcations occurring at the equilibrium sites are derived. Specifically, we obtained transcritical, pitchfork, and saddle-node bifurcation. Numerical simulations are employed to validate the theoretical study and ascertain the minimum therapy dosage necessary for eradicating cancer in the presence of psychological distress, thereby mitigating harm to patients. Fear could be a significant contributor to the spread of tumors and weakness of immune functionality.
{"title":"The effect of a psychological scare on the dynamics of the tumor-immune interaction with optimal control strategy","authors":"Rafel Ibrahim Salih, S. Jawad, K. Dehingia, Anusmita Das","doi":"10.11121/ijocta.1520","DOIUrl":"https://doi.org/10.11121/ijocta.1520","url":null,"abstract":"Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how chemotherapy and anxiety work together to affect the speed at which cancer cells multiply and the immune system’s response model is necessary to come up with ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological scare and chemotherapy on the interaction of cancer and immunity. The proposed model is accurately described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish three equilibrium positions. The stability analysis reveals that all equilibrium points consistently exhibit stability under the defined conditions. The bifurcations occurring at the equilibrium sites are derived. Specifically, we obtained transcritical, pitchfork, and saddle-node bifurcation. Numerical simulations are employed to validate the theoretical study and ascertain the minimum therapy dosage necessary for eradicating cancer in the presence of psychological distress, thereby mitigating harm to patients. Fear could be a significant contributor to the spread of tumors and weakness of immune functionality.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"22 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141806262","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}
In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.
{"title":"Design optimal neural network based on new LM training algorithm for solving 3D - PDEs","authors":"Farah F. Ghazi, L. Tawfiq","doi":"10.11121/ijocta.1519","DOIUrl":"https://doi.org/10.11121/ijocta.1519","url":null,"abstract":"In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":" 459","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823583","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}
Linear second-order cone programming (SOCP) deals with optimization problems characterized by a linear objective function and a feasible region defined by linear equalities and second-order cone constraints. These constraints involve the norm of a linear combination of variables, enabling the representation of a wide range of convex sets. The SOCP serves as a potent tool for addressing optimization challenges across engineering, finance, machine learning, and various other domains. In this paper, we introduce new optimality conditions tailored for {SOCP} problems. These conditions have the form of two optimality criteria that are obtained without the requirement of any constraint qualifications and are defined explicitly. The first criterion utilizes the concept of immobile indices of constraints. The second criterion, without relying explicitly on immobile indices, introduces a special finite vector set for assessing optimality. To demonstrate the effectiveness of these criteria, we present two illustrative examples highlighting their applicability. We compare the obtained criteria with other known optimality conditions and show the advantage of the former ones.
{"title":"Exploring constraint qualification-free optimality conditions for linear second-order cone programming","authors":"O. Kostyukova, T. Tchemisova","doi":"10.11121/ijocta.1421","DOIUrl":"https://doi.org/10.11121/ijocta.1421","url":null,"abstract":"Linear second-order cone programming (SOCP) deals with optimization problems characterized by a linear objective function and a feasible region defined by linear equalities and second-order cone constraints. These constraints involve the norm of a linear combination of variables, enabling the representation of a wide range of convex sets. The SOCP serves as a potent tool for addressing optimization challenges across engineering, finance, machine learning, and various other domains. In this paper, we introduce new optimality conditions tailored for {SOCP} problems. These conditions have the form of two optimality criteria that are obtained without the requirement of any constraint qualifications and are defined explicitly. The first criterion utilizes the concept of immobile indices of constraints. The second criterion, without relying explicitly on immobile indices, introduces a special finite vector set for assessing optimality. To demonstrate the effectiveness of these criteria, we present two illustrative examples highlighting their applicability. We compare the obtained criteria with other known optimality conditions and show the advantage of the former ones.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"78 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653120","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}
The partial neutral functional fractional differential equation described by the fractional operator is considered in the present investigation. The used fractional operator is the Caputo derivative. In the present paper, the fractional resolvent operators have been defined and used to prove the existence of the unique solution of the fractional neutral differential equations. The fixed point theorem has been used in existence investigations. For an illustration of our results in this paper, an example has been provided as well.
{"title":"Existence and uniqueness study for partial neutral functional fractional differential equation under Caputo derivative","authors":"N. Sene, A. Ndiaye","doi":"10.11121/ijocta.1464","DOIUrl":"https://doi.org/10.11121/ijocta.1464","url":null,"abstract":"The partial neutral functional fractional differential equation described by the fractional operator is considered in the present investigation. The used fractional operator is the Caputo derivative. In the present paper, the fractional resolvent operators have been defined and used to prove the existence of the unique solution of the fractional neutral differential equations. The fixed point theorem has been used in existence investigations. For an illustration of our results in this paper, an example has been provided as well.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"62 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653165","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}
Time-delay fractional optimal control problems (OCPs) are an important research area for developing effective control and optimization strategies to address complex phenomena occurring in various natural sciences, such as physics, chemistry, biology, and engineering. By considering fractional OCPs with time delays, we can design control strategies that take into account the system's history and optimize its behavior over a given time horizon. However, applying the Pontryagin principle of maximization to solve these problems leads to a boundary value problem (BVP) that includes delay and advance terms, making analytical solutions difficult and demanding. To address this issue, this paper presents a precise finite difference formula to solve the aforementioned advance-delay BVP numerically. The suggested approximate method's error analysis and convergence properties are provided, and several illustrative examples demonstrate the applicability, validity, and accuracy of the proposed approach. Simulation results confirm the proposed technique's advantages for the optimal control of delay fractional dynamical equations.
{"title":"An accurate finite difference formula for the numerical solution of delay-dependent fractional optimal control problems","authors":"D. Băleanu, M. Hajipour, A. Jajarmi","doi":"10.11121/ijocta.1478","DOIUrl":"https://doi.org/10.11121/ijocta.1478","url":null,"abstract":"Time-delay fractional optimal control problems (OCPs) are an important research area for developing effective control and optimization strategies to address complex phenomena occurring in various natural sciences, such as physics, chemistry, biology, and engineering. By considering fractional OCPs with time delays, we can design control strategies that take into account the system's history and optimize its behavior over a given time horizon. However, applying the Pontryagin principle of maximization to solve these problems leads to a boundary value problem (BVP) that includes delay and advance terms, making analytical solutions difficult and demanding. To address this issue, this paper presents a precise finite difference formula to solve the aforementioned advance-delay BVP numerically. The suggested approximate method's error analysis and convergence properties are provided, and several illustrative examples demonstrate the applicability, validity, and accuracy of the proposed approach. Simulation results confirm the proposed technique's advantages for the optimal control of delay fractional dynamical equations.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"52 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653253","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}
In this study, we introduce some new mappings in connection with Hermite-Hadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain certain new inequalities of the Fejer type that provide refinements of the Hermite-Hadamard and Fejer type integral inequalities that have already been obtained.
在本研究中，我们引入了一些与赫尔米特-哈达马德和费耶型积分不等式相关的新映射，这些不等式已利用 GA 凸函数证明。因此，我们得到了某些新的 Fejer 型不等式，这些不等式是对已得到的 Hermite-Hadamard 和 Fejer 型积分不等式的完善。
{"title":"Further refinements and inequalities of Fejer's type via GA-convexity","authors":"Muhammad Amer Latif, H. Budak, A. Kashuri","doi":"10.11121/ijocta.1482","DOIUrl":"https://doi.org/10.11121/ijocta.1482","url":null,"abstract":"In this study, we introduce some new mappings in connection with Hermite-Hadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain certain new inequalities of the Fejer type that provide refinements of the Hermite-Hadamard and Fejer type integral inequalities that have already been obtained.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"39 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141655289","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}
The purpose of this paper is the study of the eigenvalues of the second order fuzzy boundary value problem (FBVP). By using the (alpha-beta)-level set of intuitionistic fuzzy numbers and Zadeh's extension principle, the FBVP is solved with the proposed method. Furthermore, a numerical example is illustrated and the advantages of the proposed approach are compared with other well-known methods such as the solutions based on the generalized Hukuhara derivative.
{"title":"Intuitionistic fuzzy eigenvalue problem","authors":"Tahir Ceylan","doi":"10.11121/ijocta.1471","DOIUrl":"https://doi.org/10.11121/ijocta.1471","url":null,"abstract":"The purpose of this paper is the study of the eigenvalues of the second order fuzzy boundary value problem (FBVP). By using the (alpha-beta)-level set of intuitionistic fuzzy numbers and Zadeh's extension principle, the FBVP is solved with the proposed method. Furthermore, a numerical example is illustrated and the advantages of the proposed approach are compared with other well-known methods such as the solutions based on the generalized Hukuhara derivative.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"20 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653643","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}
In this study operating room scheduling (ORS) problem is addressed in multi-resource manner. In the addressed problem, besides operating rooms (ORs) and surgeons, the anesthesia team is also considered as an additional resource. The surgeon(s) who will perform the operation have already been assigned to the patients and is a dedicated resource. The assignment of the anesthesia team has been considered as a decision problem and a flexible resource. In this study, cooperative operations are also considered. A mixed integer linear programming (MILP) model is proposed for the problem. Since the problem is NP-hard, an artificial bee colony (ABC) algorithm is proposed for the problem. The solutions of the ABC are compared with the MILP model and random search.
{"title":"Artificial bee colony algorithm for operating room scheduling problem with dedicated/flexible resources and cooperative operations","authors":"G. Bektur, Hatice Kübra Aslan","doi":"10.11121/ijocta.1466","DOIUrl":"https://doi.org/10.11121/ijocta.1466","url":null,"abstract":"In this study operating room scheduling (ORS) problem is addressed in multi-resource manner. In the addressed problem, besides operating rooms (ORs) and surgeons, the anesthesia team is also considered as an additional resource. The surgeon(s) who will perform the operation have already been assigned to the patients and is a dedicated resource. The assignment of the anesthesia team has been considered as a decision problem and a flexible resource. In this study, cooperative operations are also considered. A mixed integer linear programming (MILP) model is proposed for the problem. Since the problem is NP-hard, an artificial bee colony (ABC) algorithm is proposed for the problem. The solutions of the ABC are compared with the MILP model and random search.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"51 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653177","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}
In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grünwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a non-porous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow.
{"title":"Fractional model for blood flow under MHD influence in porous and non-porous media","authors":"Fatma Ayaz, Kubra Heredag","doi":"10.11121/ijocta.1497","DOIUrl":"https://doi.org/10.11121/ijocta.1497","url":null,"abstract":"In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grünwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a non-porous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":" 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140681377","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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