Iffatricia Haura Febiriana, Abdullah Hasan Hassan, D. Aldila
This paper focuses on the impact of mosquito biting bias on the success of malaria intervention strategies. The initial model is developed considering the existence of symptomatic and asymptomatic humans, as well as vector bias. The model is then analyzed to demonstrate how the malaria-endemic equilibrium always exists and is globally asymptotically stable if the basic reproduction number is larger than one. On the other hand, malaria will always go extinct in the population if the basic reproduction number is less than one. For intervention analysis, the model is extended by considering mosquito repellent and hospitalization as control strategies. The control reproduction number is shown analytically. Using the Pontryagin maximum principle, we characterize our optimal control problem. Several scenarios are conducted to observe the dynamics of control variables under different circumstances. We found that the intervention of mosquito repellent and hospitalization together is the most cost-effective strategy to reduce the spread of malaria. Furthermore, we have shown that the more biased the vector attracted to infected individuals, the higher the cost needed to implement the control strategy.
{"title":"Enhancing Malaria Control Strategy: Optimal Control and Cost-Effectiveness Analysis on the Impact of Vector Bias on the Efficacy of Mosquito Repellent and Hospitalization","authors":"Iffatricia Haura Febiriana, Abdullah Hasan Hassan, D. Aldila","doi":"10.1155/2024/9943698","DOIUrl":"https://doi.org/10.1155/2024/9943698","url":null,"abstract":"This paper focuses on the impact of mosquito biting bias on the success of malaria intervention strategies. The initial model is developed considering the existence of symptomatic and asymptomatic humans, as well as vector bias. The model is then analyzed to demonstrate how the malaria-endemic equilibrium always exists and is globally asymptotically stable if the basic reproduction number is larger than one. On the other hand, malaria will always go extinct in the population if the basic reproduction number is less than one. For intervention analysis, the model is extended by considering mosquito repellent and hospitalization as control strategies. The control reproduction number is shown analytically. Using the Pontryagin maximum principle, we characterize our optimal control problem. Several scenarios are conducted to observe the dynamics of control variables under different circumstances. We found that the intervention of mosquito repellent and hospitalization together is the most cost-effective strategy to reduce the spread of malaria. Furthermore, we have shown that the more biased the vector attracted to infected individuals, the higher the cost needed to implement the control strategy.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"3 19","pages":"9943698:1-9943698:17"},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140241434","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}
Aliaa Burqan, M. Khandaqji, Z. Al-Zhour, Ahmad El-Ajou, Tasneem Alrahamneh
The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method.
{"title":"Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique","authors":"Aliaa Burqan, M. Khandaqji, Z. Al-Zhour, Ahmad El-Ajou, Tasneem Alrahamneh","doi":"10.1155/2024/7835548","DOIUrl":"https://doi.org/10.1155/2024/7835548","url":null,"abstract":"The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. In this paper, we reformulate this problem in the sense of Caputo fractional derivative, whose physical meanings, in this case, are very evident by describing the whole time domain of physical processing. The main aim of this work is to present the analytical approximate series for the nonlinear Caputo fractional KdV-Burgers equation by applying the Laplace residual power series method. The main tools of this method are the Laplace transform, Laurent series, and residual function. Moreover, four attractive and satisfying applications are given and solved to elucidate the mechanism of our proposed method. The analytical approximate series solution via this sweet technique shows excellent agreement with the solution obtained from other methods in simple and understandable steps. Finally, graphical and numerical comparison results at different values of α are provided with residual and relative errors to illustrate the behaviors of the approximate results and the effectiveness of the proposed method.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"16 19","pages":"7835548:1-7835548:19"},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140258033","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, an efficient new technique is used for solving nonlinear fractional problems that satisfy specific criteria. This technique is referred to as the double conformable fractional Laplace-Elzaki decomposition method (DCFLEDM). This approach combines the double Laplace-Elzaki transform method with the Adomian decomposition method. The fundamental concepts and findings of the recently suggested transformation are presented. For the purpose of assessing the accuracy of our approach, we provide three examples and introduce the series solutions of these equations using DCLEDM. The results show that the proposed strategy is a very effective, reliable, and efficient approach for addressing nonlinear fractional problems using the conformable derivative.
{"title":"An Efficient New Technique for Solving Nonlinear Problems Involving the Conformable Fractional Derivatives","authors":"Shams A. Ahmed","doi":"10.1155/2024/5958560","DOIUrl":"https://doi.org/10.1155/2024/5958560","url":null,"abstract":"In this paper, an efficient new technique is used for solving nonlinear fractional problems that satisfy specific criteria. This technique is referred to as the double conformable fractional Laplace-Elzaki decomposition method (DCFLEDM). This approach combines the double Laplace-Elzaki transform method with the Adomian decomposition method. The fundamental concepts and findings of the recently suggested transformation are presented. For the purpose of assessing the accuracy of our approach, we provide three examples and introduce the series solutions of these equations using DCLEDM. The results show that the proposed strategy is a very effective, reliable, and efficient approach for addressing nonlinear fractional problems using the conformable derivative.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"160 1","pages":"5958560:1-5958560:17"},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140438036","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}
With the development of industrial demand, precise identification of system models is currently required in the field of industrial control, which limits the whale search algorithm. In response to the fact that whale optimization algorithms are prone to falling into local optima and the identification of important Hammerstein models ignores the issue of noise outliers in actual industrial environments, this study improves the whale algorithm and constructs a Hammerstein model identification strategy for nonlinear systems under heavy-tailed noise using the improved whale algorithm. Results showed that it had a lower rank average and an average success rate of 95.65%. It found the global optimum when the number of iterations reached around 150 and had faster convergence speed and accuracy. In identifying Hammerstein model under heavy-tailed noise, the average prediction recognition accuracy of the improved whale algorithm was 92.38%, the determination coefficient was 0.89, the percentage fitting error was 0.03, and the system error was 0.02. This research achievement has certain value in the field of industrial control and can serve as a technical reference.
{"title":"Application of Improved WOA in Hammerstein Parameter Resolution Problems under Advanced Mathematical Theory","authors":"Lu Zhao, Jiangjun Liu, Yuan Li","doi":"10.1155/2024/5619098","DOIUrl":"https://doi.org/10.1155/2024/5619098","url":null,"abstract":"With the development of industrial demand, precise identification of system models is currently required in the field of industrial control, which limits the whale search algorithm. In response to the fact that whale optimization algorithms are prone to falling into local optima and the identification of important Hammerstein models ignores the issue of noise outliers in actual industrial environments, this study improves the whale algorithm and constructs a Hammerstein model identification strategy for nonlinear systems under heavy-tailed noise using the improved whale algorithm. Results showed that it had a lower rank average and an average success rate of 95.65%. It found the global optimum when the number of iterations reached around 150 and had faster convergence speed and accuracy. In identifying Hammerstein model under heavy-tailed noise, the average prediction recognition accuracy of the improved whale algorithm was 92.38%, the determination coefficient was 0.89, the percentage fitting error was 0.03, and the system error was 0.02. This research achievement has certain value in the field of industrial control and can serve as a technical reference.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"47 5","pages":"5619098:1-5619098:11"},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140440524","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}
As a key component of enterprise assets, accounts receivable play an important role in enterprise financial management and determine the long-term development of enterprises in the later period. In order to minimize the financial risk brought by the credit sales of enterprises, this subject studies the intelligent optimization of enterprise financial account receivable management. BP neural network and K-means clustering algorithm are used to evaluate the risk of account receivable and the owner’s credit, respectively. The account balance accounts for 45.20% of the total amount, and the risk rating of accounts receivable is 4. The training result of BP neural network algorithm has high accuracy. With K-means clustering algorithm, accurate evaluation of owner’s credit can be achieved, which can provide reference for optimization of enterprise account receivable management mode.
{"title":"Intelligent Optimization Model of Enterprise Financial Account Receivable Management","authors":"Yunxiang Peng, Guixian Tian","doi":"10.1155/2024/4961081","DOIUrl":"https://doi.org/10.1155/2024/4961081","url":null,"abstract":"As a key component of enterprise assets, accounts receivable play an important role in enterprise financial management and determine the long-term development of enterprises in the later period. In order to minimize the financial risk brought by the credit sales of enterprises, this subject studies the intelligent optimization of enterprise financial account receivable management. BP neural network and K-means clustering algorithm are used to evaluate the risk of account receivable and the owner’s credit, respectively. The account balance accounts for 45.20% of the total amount, and the risk rating of accounts receivable is 4. The training result of BP neural network algorithm has high accuracy. With K-means clustering algorithm, accurate evaluation of owner’s credit can be achieved, which can provide reference for optimization of enterprise account receivable management mode.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"101 3","pages":"4961081:1-4961081:9"},"PeriodicalIF":0.0,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140492630","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}
Based on the equivalent bending stiffness of the viscoelastic cracked beam with open cracks, the corresponding complex frequency characteristic equations of a Timoshenko viscoelastic cracked beam are obtained by using the method of separation of variables and the Laplace transform. The vibration characteristics of a viscoelastic Timoshenko cracked beams with the standard linear solid model and Kelvin-Voigt model are investigated. By numerical examples, the effects of the crack location, crack number, crack depth, and slenderness ratio on the vibration characteristics of the viscoelastic cracked beams are revealed.
{"title":"Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models","authors":"Chaoxing Fu","doi":"10.1155/2023/2341137","DOIUrl":"https://doi.org/10.1155/2023/2341137","url":null,"abstract":"Based on the equivalent bending stiffness of the viscoelastic cracked beam with open cracks, the corresponding complex frequency characteristic equations of a Timoshenko viscoelastic cracked beam are obtained by using the method of separation of variables and the Laplace transform. The vibration characteristics of a viscoelastic Timoshenko cracked beams with the standard linear solid model and Kelvin-Voigt model are investigated. By numerical examples, the effects of the crack location, crack number, crack depth, and slenderness ratio on the vibration characteristics of the viscoelastic cracked beams are revealed.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"71 1","pages":"2341137:1-2341137:11"},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80312222","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 novel coronavirus is a recently discovered member of one of the largest families of viruses with symptoms ranging from a simple cold to excruciating respiratory agony. In the present paper, a deterministic mathematical model is formulated to estimate the transmission dynamics of COVID-19 with the inclusion of control strategies like (i) double-dose vaccination, (ii) prevention, and (iii) treatment. In addition, instead of considering all infectious humans as one unit, we separate them into symptomatic and asymptomatic groups, and the impact is analyzed. This separation is meaningful because various reports indicate that the asymptomatic cases will spread the disease more than the symptomatic cases. The model is proved to be mathematically well-posed and biologically meaningful by showing positivity and boundedness of the solution using the appropriate initial conditions. For the reproduction number, a parametric formula is constructed, and also the associated numerical value is calculated from the reported real data in Ethiopia. Moreover, disease-free and endemic equilibria are determined, and their local and global stabilities are discussed using the Lyapunov function technique. These equilibria are found to be locally asymptotically stable if R 0 < 1 and R 0 > 1 , respectively. Following the model fitting and estimation of the parameter values, sensitivity analysis was performed in order to analyze the impact of each parameter on transmission dynamics. In other words, this study can be used to evaluate how major model parameters affect transmission dynamics and control. Utilizing Pontryagin’s maximal principle, the best control measures are implemented with the aim of lowering the burdens associated with infection, prevention, and treatment. To comprehend and visualize the impact of control techniques on the development of the disease and to illustrate the analytical findings generated in this study, numerical simulation studies are conducted. Finally, the output of the study illustrates that adhering to all the control strategies has a big impact on minimizing the transmission of the disease in society. Which means that if the control strategies are well managed by the concerned body, then the burden of the disease is reduced quickly in the Ethiopian population.
{"title":"Modeling and Optimal Control Analysis Applied to Real Cases of COVID-19 Pandemic with Double Dose Vaccination in Ethiopia","authors":"F. Legesse, Koya Purnachandra Rao, T. Keno","doi":"10.1155/2023/5591165","DOIUrl":"https://doi.org/10.1155/2023/5591165","url":null,"abstract":"The novel coronavirus is a recently discovered member of one of the largest families of viruses with symptoms ranging from a simple cold to excruciating respiratory agony. In the present paper, a deterministic mathematical model is formulated to estimate the transmission dynamics of COVID-19 with the inclusion of control strategies like (i) double-dose vaccination, (ii) prevention, and (iii) treatment. In addition, instead of considering all infectious humans as one unit, we separate them into symptomatic and asymptomatic groups, and the impact is analyzed. This separation is meaningful because various reports indicate that the asymptomatic cases will spread the disease more than the symptomatic cases. The model is proved to be mathematically well-posed and biologically meaningful by showing positivity and boundedness of the solution using the appropriate initial conditions. For the reproduction number, a parametric formula is constructed, and also the associated numerical value is calculated from the reported real data in Ethiopia. Moreover, disease-free and endemic equilibria are determined, and their local and global stabilities are discussed using the Lyapunov function technique. These equilibria are found to be locally asymptotically stable if \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 <\u0000 1\u0000 \u0000 and \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 >\u0000 1\u0000 \u0000 , respectively. Following the model fitting and estimation of the parameter values, sensitivity analysis was performed in order to analyze the impact of each parameter on transmission dynamics. In other words, this study can be used to evaluate how major model parameters affect transmission dynamics and control. Utilizing Pontryagin’s maximal principle, the best control measures are implemented with the aim of lowering the burdens associated with infection, prevention, and treatment. To comprehend and visualize the impact of control techniques on the development of the disease and to illustrate the analytical findings generated in this study, numerical simulation studies are conducted. Finally, the output of the study illustrates that adhering to all the control strategies has a big impact on minimizing the transmission of the disease in society. Which means that if the control strategies are well managed by the concerned body, then the burden of the disease is reduced quickly in the Ethiopian population.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"30 1","pages":"5591165:1-5591165:19"},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81523862","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 economics, we know the law of demand: a higher price will lead to a lower quantity demanded. The question is to know how much lower the quantity demanded will be. Similarly, the law of supply shows that a higher price will lead to a higher quantity supplied. Another question is to know how much higher. To find answers to these questions which are critically important in the real world, we need the concept of elasticity. Elasticity is an economics concept that measures the responsiveness of one variable to changes in another variable. Elasticity is a function e x that can be built from an arbitrary function y = g x . Elasticity at a certain point is usually calculated as e x = d y / d x x / y . Elasticity can be expressed in many forms. An interesting form, from an economic point of view, is the ratio between the derivative of the logarithm of the distribution function with respect to the logarithm of the point x , which is developed in this article. The aim of this article is to study the direction of variation of this elasticity function and to construct a nonparametric estimator because the estimators that have been constructed so far are parametric estimators and admit many deficiencies in practice. And finally, we study the strong consistency of the said estimator. A numerical study was carried out to verify the adequacy of the theory.
在经济学中，我们知道需求定律:更高的价格将导致更低的需求量。问题是要知道需求量会降低多少。同样，供给定律表明，较高的价格将导致较高的供给量。另一个问题是要知道高了多少。为了找到这些在现实世界中至关重要的问题的答案，我们需要弹性的概念。弹性是一个经济学概念，用来衡量一个变量对另一个变量变化的响应性。弹性是一个函数ex，它可以由任意函数y = gx构建。某一点的弹性通常计算为e x = d y / d x x / y。弹性可以用多种形式表示。从经济学的角度来看，一个有趣的形式是分布函数的对数的导数与点x的对数的比值，这在本文中得到了推导。本文的目的是研究该弹性函数的变化方向，并构造一个非参数估计量，因为迄今为止构造的估计量都是参数估计量，在实践中存在许多不足。最后，研究了该估计量的强相合性。为了验证理论的充分性，进行了数值研究。
{"title":"On the Nature of Elasticity Function: An Investigation and a Kernel Estimation","authors":"K. Agbokou","doi":"10.1155/2023/1346602","DOIUrl":"https://doi.org/10.1155/2023/1346602","url":null,"abstract":"In economics, we know the law of demand: a higher price will lead to a lower quantity demanded. The question is to know how much lower the quantity demanded will be. Similarly, the law of supply shows that a higher price will lead to a higher quantity supplied. Another question is to know how much higher. To find answers to these questions which are critically important in the real world, we need the concept of elasticity. Elasticity is an economics concept that measures the responsiveness of one variable to changes in another variable. Elasticity is a function \u0000 \u0000 e\u0000 \u0000 \u0000 x\u0000 \u0000 \u0000 \u0000 that can be built from an arbitrary function \u0000 \u0000 y\u0000 =\u0000 g\u0000 \u0000 \u0000 x\u0000 \u0000 \u0000 \u0000 . Elasticity at a certain point is usually calculated as \u0000 \u0000 e\u0000 \u0000 \u0000 x\u0000 \u0000 \u0000 =\u0000 \u0000 \u0000 d\u0000 y\u0000 /\u0000 d\u0000 x\u0000 \u0000 \u0000 \u0000 \u0000 x\u0000 /\u0000 y\u0000 \u0000 \u0000 \u0000 . Elasticity can be expressed in many forms. An interesting form, from an economic point of view, is the ratio between the derivative of the logarithm of the distribution function with respect to the logarithm of the point \u0000 \u0000 x\u0000 \u0000 , which is developed in this article. The aim of this article is to study the direction of variation of this elasticity function and to construct a nonparametric estimator because the estimators that have been constructed so far are parametric estimators and admit many deficiencies in practice. And finally, we study the strong consistency of the said estimator. A numerical study was carried out to verify the adequacy of the theory.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"29 1","pages":"1346602:1-1346602:14"},"PeriodicalIF":0.0,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82752999","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 provides asymptotic expansions for large values of of tangent and Apostol-tangent polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.
这篇文章provides asymptotic expansions for大的价值观 n 切线的 T n μz 和Apostol-tangent T n μz ;λ polynomials情结的订单。衍射是使用引物与引物切割的例子进行的。
{"title":"Asymptotic Expansions for Large Degree Tangent and Apostol-Tangent Polynomials of Complex Order","authors":"C. Corcino, R. Corcino, Jeremar Casquejo","doi":"10.1155/2023/9917885","DOIUrl":"https://doi.org/10.1155/2023/9917885","url":null,"abstract":"<jats:p>This paper provides asymptotic expansions for large values of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>n</mi>\u0000 </math>\u0000 </jats:inline-formula> of tangent <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>z</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> and Apostol-tangent <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>z</mi>\u0000 <mo>;</mo>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.</jats:p>","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"6 1","pages":"9917885:1-9917885:8"},"PeriodicalIF":0.0,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78418693","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}
We intend to analyze the consequence of considering thermal radiation on time-dependent flow of the Casson fluid due to an exponentially accelerated inclined surface along with thermal as well as solutal convective boundary conditions. Fundamental equations governing an isotropic incompressible radiative Casson fluid flow are defined through a set of linear partial differential equations, and exact solutions are derived by using the Laplace transform approach. The numerical findings, obtained using MATLAB software, are presented in graphical and tabular representations based on the obtained analytical solutions of the fundamental equations. This investigation shows that the increment in thermal radiation results in the increment in fluid velocity and temperature distribution including thermal and momentum boundary layer thicknesses. Most interestingly, increasing the mass transfer coefficient results in an increment in the species concentration, velocity profiles, and mass transfer rate. However, the fluid velocity diminishes near the plate upon the increase in plate inclination. The scientific community will benefit greatly from this work since the findings can serve as benchmark solutions using numerical approaches to solve fully nonlinear flow governing problems.
{"title":"Modeling and Analysis of Unsteady Casson Fluid Flow due to an Exponentially Accelerating Plate with Thermal and Solutal Convective Boundary Conditions","authors":"M. Endalew, S. Sarkar","doi":"10.1155/2023/3065357","DOIUrl":"https://doi.org/10.1155/2023/3065357","url":null,"abstract":"We intend to analyze the consequence of considering thermal radiation on time-dependent flow of the Casson fluid due to an exponentially accelerated inclined surface along with thermal as well as solutal convective boundary conditions. Fundamental equations governing an isotropic incompressible radiative Casson fluid flow are defined through a set of linear partial differential equations, and exact solutions are derived by using the Laplace transform approach. The numerical findings, obtained using MATLAB software, are presented in graphical and tabular representations based on the obtained analytical solutions of the fundamental equations. This investigation shows that the increment in thermal radiation results in the increment in fluid velocity and temperature distribution including thermal and momentum boundary layer thicknesses. Most interestingly, increasing the mass transfer coefficient results in an increment in the species concentration, velocity profiles, and mass transfer rate. However, the fluid velocity diminishes near the plate upon the increase in plate inclination. The scientific community will benefit greatly from this work since the findings can serve as benchmark solutions using numerical approaches to solve fully nonlinear flow governing problems.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"78 2 1","pages":"3065357:1-3065357:13"},"PeriodicalIF":0.0,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87908764","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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