G. Loaiza, Y. Acevedo, O. Duque, Danilo A. García Hernández
We obtain the optimal system’s generating operators associated with a generalized Levinson–Smith equation; this one is related to the Lienard equation which is important for physical, mathematical, and engineering points of view. The underlying equation has applications in mechanics and nonlinear dynamics as well. This equation has been widely studied in the qualitative scheme. Here, we treat the equation by using the Lie group method, and we obtain certain operators; using those operators, we characterized all invariants solutions associated with the generalized equation of Levinson Smith considered in this paper. Finally, we classify the Lie algebra associated with the given equation.
{"title":"Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation","authors":"G. Loaiza, Y. Acevedo, O. Duque, Danilo A. García Hernández","doi":"10.1155/2021/6628243","DOIUrl":"https://doi.org/10.1155/2021/6628243","url":null,"abstract":"We obtain the optimal system’s generating operators associated with a generalized Levinson–Smith equation; this one is related to the Lienard equation which is important for physical, mathematical, and engineering points of view. The underlying equation has applications in mechanics and nonlinear dynamics as well. This equation has been widely studied in the qualitative scheme. Here, we treat the equation by using the Lie group method, and we obtain certain operators; using those operators, we characterized all invariants solutions associated with the generalized equation of Levinson Smith considered in this paper. Finally, we classify the Lie algebra associated with the given equation.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44935246","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 work, we study the sufficient condition for convergence of the reduced differential transform method for nonlinear differential equations. The main power of this method is its ability and flexibility in solving linear and nonlinear problems properly and easily and obtain solutions both numerically and analytically. Simple approaches of reduced differential transform method and the convergence results for different classes of differential equations such as linear and nonlinear ordinary, partial, fractional, and system of differential equations are briefly discussed. Eight examples are checked to confirm convergence results as well as the strength and efficiency of the method.
{"title":"Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations","authors":"Seyyedeh Roodabeh Moosavi Noori, N. Taghizadeh","doi":"10.1155/2021/6696414","DOIUrl":"https://doi.org/10.1155/2021/6696414","url":null,"abstract":"In this work, we study the sufficient condition for convergence of the reduced differential transform method for nonlinear differential equations. The main power of this method is its ability and flexibility in solving linear and nonlinear problems properly and easily and obtain solutions both numerically and analytically. Simple approaches of reduced differential transform method and the convergence results for different classes of differential equations such as linear and nonlinear ordinary, partial, fractional, and system of differential equations are briefly discussed. Eight examples are checked to confirm convergence results as well as the strength and efficiency of the method.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47192491","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 paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. We compare the results obtained using this approach to the standard finite element approach. +e proposed method is adequate even with the singular right-hand side of type Dirac.
{"title":"A New Numerical Method to Solve Some \u0000 \u0000 \u0000 PDE\u0000 \u0000 \u0000 s\u0000 \u0000 \u0000 in the Unit Ball and Comparison with the Finite Element and the Exact Solution","authors":"R. Malek, C. Ziti","doi":"10.1155/2021/6696165","DOIUrl":"https://doi.org/10.1155/2021/6696165","url":null,"abstract":"In this paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. We compare the results obtained using this approach to the standard finite element approach. +e proposed method is adequate even with the singular right-hand side of type Dirac.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":"1-15"},"PeriodicalIF":1.6,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46894295","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}
Salamida Daudi, L. Luboobi, M. Kgosimore, Dmitry Kuznetsov
In this paper, we propose and analyze a stage-structured mathematical model for modelling the control of the impact of Fall Armyworm infestations on maize production. Preliminary analysis of the model in the vegetative and reproductive stages revealed that the two systems had a unique and positively bounded solution for all time . Numerical analysis of the model in both stages under two different cases was also considered: Case 1: different number of the adult moths in the field assumed at and Case 2: the existence of exogenous factors that lead to the immigration of adult moths in the field at time . The results indicate that the destruction of maize biomass which is accompanied by a decrease in maize plants to an average of 160 and 142 in the vegetative and reproductive stages, respectively, was observed to be higher in Case 2 than in Case 1 due to subsequent increase in egg production and density of the caterpillars in first few (10) days after immigration. This severe effect on maize plants caused by the unprecedented number of the pests influenced the extension of the model in both stages to include controls such as pesticides and harvesting. The results further show that the pest was significantly suppressed, resulting in an increase in maize plants to an average of 467 and 443 in vegetative and reproductive stages, respectively.
{"title":"Modelling the Control of the Impact of Fall Armyworm (Spodoptera frugiperda) Infestations on Maize Production","authors":"Salamida Daudi, L. Luboobi, M. Kgosimore, Dmitry Kuznetsov","doi":"10.1155/2021/8838089","DOIUrl":"https://doi.org/10.1155/2021/8838089","url":null,"abstract":"In this paper, we propose and analyze a stage-structured mathematical model for modelling the control of the impact of Fall Armyworm infestations on maize production. Preliminary analysis of the model in the vegetative and reproductive stages revealed that the two systems had a unique and positively bounded solution for all time . Numerical analysis of the model in both stages under two different cases was also considered: Case 1: different number of the adult moths in the field assumed at and Case 2: the existence of exogenous factors that lead to the immigration of adult moths in the field at time . The results indicate that the destruction of maize biomass which is accompanied by a decrease in maize plants to an average of 160 and 142 in the vegetative and reproductive stages, respectively, was observed to be higher in Case 2 than in Case 1 due to subsequent increase in egg production and density of the caterpillars in first few (10) days after immigration. This severe effect on maize plants caused by the unprecedented number of the pests influenced the extension of the model in both stages to include controls such as pesticides and harvesting. The results further show that the pest was significantly suppressed, resulting in an increase in maize plants to an average of 467 and 443 in vegetative and reproductive stages, respectively.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":"1-16"},"PeriodicalIF":1.6,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45137906","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}
This paper studies and investigates total stability results of a class of dynamic systems within a prescribed closed ball of the state space around the origin. The class of systems under study includes unstructured nonlinearities subject to multiple higher-order Lipschitz-type conditions which influence the dynamics and which can be eventually interpreted as unstructured perturbations. The results are also extended to the case of presence of multiple internal (i.e., in the state) point discrete delays. Some stability extensions are also discussed for the case when the systems are subject to forcing efforts by using links between the controllability and stabilizability concepts from control theory and the existence of stabilizing linear controls. The results are based on the ad hoc use of Gronwall’s inequality.
{"title":"About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays","authors":"M. de La Sen","doi":"10.1155/2021/5593813","DOIUrl":"https://doi.org/10.1155/2021/5593813","url":null,"abstract":"This paper studies and investigates total stability results of a class of dynamic systems within a prescribed closed ball of the state space around the origin. The class of systems under study includes unstructured nonlinearities subject to multiple higher-order Lipschitz-type conditions which influence the dynamics and which can be eventually interpreted as unstructured perturbations. The results are also extended to the case of presence of multiple internal (i.e., in the state) point discrete delays. Some stability extensions are also discussed for the case when the systems are subject to forcing efforts by using links between the controllability and stabilizability concepts from control theory and the existence of stabilizing linear controls. The results are based on the ad hoc use of Gronwall’s inequality.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":"1-12"},"PeriodicalIF":1.6,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47314992","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}
This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.
{"title":"Modeling the Effect of External Computers and Removable Devices on a Computer Network with Heterogeneous Immunity","authors":"Walaa S. Bahashwan, Salma M. Al-Tuwairqi","doi":"10.1155/2021/6694098","DOIUrl":"https://doi.org/10.1155/2021/6694098","url":null,"abstract":"This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"6 4","pages":"1-13"},"PeriodicalIF":1.6,"publicationDate":"2021-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41243402","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 COVID-19 pandemic has put the world in threat for a long time It was first identified in Wuhan, China, in December 2019 and has been declared a pandemic by the WHO This disease is mainly caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) So far, no vaccine or medicine has been developed for the proper treatment of this disease, so people are afraid of getting infected The pandemic has placed many nations at the door of socioeconomic emergencies Therefore, it is very important to predict the development trend of this epidemic, and we know mathematical modelling is a basic tool to research the dynamic behaviour of disease and predict the spreading trend of the disease In this study, we have formulated a mathematical model for the COVID-19 outbreak by introducing a quarantine class with media-induced fear in the disease transmission rate to analyze the dynamic behaviour of this epidemic We have calculated the basic reproduction number R0, and we observed that when R0 1, then the system is permanent and there exists a unique endemic equilibrium point Global stability of the endemic equilibrium point is developed by using Li and Muldowney's high-dimensional Bendixson criterion Finally, some numerical simulations are performed using MATLAB to verify our analytical results [ABSTRACT FROM AUTHOR] Copyright of International Journal of Differential Equations is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )
{"title":"Impact of Media-Induced Fear on the Control of COVID-19 Outbreak: A Mathematical Study","authors":"C. Maji","doi":"10.1155/2021/2129490","DOIUrl":"https://doi.org/10.1155/2021/2129490","url":null,"abstract":"The COVID-19 pandemic has put the world in threat for a long time It was first identified in Wuhan, China, in December 2019 and has been declared a pandemic by the WHO This disease is mainly caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) So far, no vaccine or medicine has been developed for the proper treatment of this disease, so people are afraid of getting infected The pandemic has placed many nations at the door of socioeconomic emergencies Therefore, it is very important to predict the development trend of this epidemic, and we know mathematical modelling is a basic tool to research the dynamic behaviour of disease and predict the spreading trend of the disease In this study, we have formulated a mathematical model for the COVID-19 outbreak by introducing a quarantine class with media-induced fear in the disease transmission rate to analyze the dynamic behaviour of this epidemic We have calculated the basic reproduction number R0, and we observed that when R0 1, then the system is permanent and there exists a unique endemic equilibrium point Global stability of the endemic equilibrium point is developed by using Li and Muldowney's high-dimensional Bendixson criterion Finally, some numerical simulations are performed using MATLAB to verify our analytical results [ABSTRACT FROM AUTHOR] Copyright of International Journal of Differential Equations is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47500241","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, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order .
{"title":"Fuzzy Conformable Fractional Differential Equations","authors":"A. Harir, S. Melliani, L. S. Chadli","doi":"10.1155/2021/6655450","DOIUrl":"https://doi.org/10.1155/2021/6655450","url":null,"abstract":"In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order .","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":"1-6"},"PeriodicalIF":1.6,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43253571","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}
This paper systematically investigates the Lie group analysis method of the time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions of the time-fractional (RLW) equation are obtained. It is shown that the governing equation can be transformed into a fractional ordinary differential equation with a new independent variable, where the fractional derivatives are in Erdelyi–Kober sense. Furthermore, the explicit analytic solutions of the time-fractional (RLW) equation are obtained using the power series expansion method. Finally, some graphical features were presented to give a visual interpretation of the solutions.
{"title":"Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation","authors":"N. Maarouf, Hicham Maadan, K. Hilal","doi":"10.1155/2021/6614231","DOIUrl":"https://doi.org/10.1155/2021/6614231","url":null,"abstract":"This paper systematically investigates the Lie group analysis method of the time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions of the time-fractional (RLW) equation are obtained. It is shown that the governing equation can be transformed into a fractional ordinary differential equation with a new independent variable, where the fractional derivatives are in Erdelyi–Kober sense. Furthermore, the explicit analytic solutions of the time-fractional (RLW) equation are obtained using the power series expansion method. Finally, some graphical features were presented to give a visual interpretation of the solutions.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49264931","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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