Khuram Ali Khan, Saeeda Fatima, Ammara Nosheen, Rostin Matendo Mabela
In this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are -convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions whose absolute values of second derivatives are -convex are also established with the help of an existing identity in literature. Many limiting results are deduced from the main results which are stated in remarks. Some applications of proved results are also discussed in the present study.
{"title":"New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals","authors":"Khuram Ali Khan, Saeeda Fatima, Ammara Nosheen, Rostin Matendo Mabela","doi":"10.1155/2024/1997549","DOIUrl":"https://doi.org/10.1155/2024/1997549","url":null,"abstract":"In this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 4.9929 6.1673\" width=\"4.9929pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions whose absolute values of second derivatives are <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 4.9929 6.1673\" width=\"4.9929pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-116\"></use></g></svg>-</span>convex are also established with the help of an existing identity in literature. Many limiting results are deduced from the main results which are stated in remarks. Some applications of proved results are also discussed in the present study.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139476486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Sudarmozhi, D. Iranian, M. M. Alqarni, Muhammad Sabeel Khan, Emad E. Mahmoud, R. Pradhan, M. M. Haque
This study aims to bridge the gap by conducting a numerical analysis of Maxwell fluid behaviour on a perpendicular plate within a porous medium, considering both chemical reaction and heat generation. The investigation also encompasses the study of energy and mass transfer within magnetohydrodynamic (MHD) Maxwell fluids. We utilise a transformation technique employing similarity variables to address the challenge posed by the nonlinear partial differential equations (PDEs). These transformed equations are subsequently solved via the bvp4c solver in MATLAB. The obtained results exhibit a high degree of agreement with the previously published work. The study systematically explores the influence of chemical reaction, energy generation, and Deborah number parameters on temperature and velocity, as well as concentration, presenting the outcomes graphically. In addition, we calculate local Sherwood numbers, Nusselt numbers, and skin friction coefficients to assess the impact of chemical reactions. Our findings notably indicate that Sherwood numbers and skin friction coefficients increase with higher levels of chemical reaction, while local Nusselt numbers decrease as chemical reactions become more pronounced. By studying Maxwell fluid flow over a perpendicular plate with chemical reactions, this research contributes to optimizing processes, enhancing product quality, and providing deeper insights into the behaviour of complex fluids in real-world scenarios.
{"title":"Exploring the Steady Flow of a Viscoelastic Fluid Passing over a Porous Perpendicular Plate Subjected to Heat Generation and Chemical Reactions","authors":"K. Sudarmozhi, D. Iranian, M. M. Alqarni, Muhammad Sabeel Khan, Emad E. Mahmoud, R. Pradhan, M. M. Haque","doi":"10.1155/2024/6947400","DOIUrl":"https://doi.org/10.1155/2024/6947400","url":null,"abstract":"This study aims to bridge the gap by conducting a numerical analysis of Maxwell fluid behaviour on a perpendicular plate within a porous medium, considering both chemical reaction and heat generation. The investigation also encompasses the study of energy and mass transfer within magnetohydrodynamic (MHD) Maxwell fluids. We utilise a transformation technique employing similarity variables to address the challenge posed by the nonlinear partial differential equations (PDEs). These transformed equations are subsequently solved via the bvp4c solver in MATLAB. The obtained results exhibit a high degree of agreement with the previously published work. The study systematically explores the influence of chemical reaction, energy generation, and Deborah number parameters on temperature and velocity, as well as concentration, presenting the outcomes graphically. In addition, we calculate local Sherwood numbers, Nusselt numbers, and skin friction coefficients to assess the impact of chemical reactions. Our findings notably indicate that Sherwood numbers and skin friction coefficients increase with higher levels of chemical reaction, while local Nusselt numbers decrease as chemical reactions become more pronounced. By studying Maxwell fluid flow over a perpendicular plate with chemical reactions, this research contributes to optimizing processes, enhancing product quality, and providing deeper insights into the behaviour of complex fluids in real-world scenarios.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let be a commutative ring with nonzero identity, be a multiplicatively closed subset of , and be a unital -module. In this article, we introduce the concepts of -semiannihilator small submodules and --small submodules as generalizations of
In this paper, integer- and fractional-order models are discussed to investigate the dynamics of malaria in a human host with a varied age distribution. A system of differential equation model with five human state variables and two mosquito state variables was examined. Preschool-age (0–5) and young-age individuals make up our model’s division of the human population. We investigated the existence of an area in which the model is both mathematically and epidemiologically well posed. According to the findings of our mathematical research, the disease-free equilibrium exists whenever the fundamental reproduction number is smaller than one and is asymptotically stable. The disease-free equilibrium point is unstable when . We showed that the endemic equilibrium point is unique for . Also, the most influential control parameters of the spread of malaria were identified. Numerical simulations of both classical and fractional order were conducted, and we used ODE (45) for classical part and numerical technique developed by Toufik and Atangana for fractional order. The infected population
{"title":"Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana–Baleanu Fractional Operators","authors":"Dawit Kechine Menbiko, Chernet Tuge Deressa","doi":"10.1155/2024/6652037","DOIUrl":"https://doi.org/10.1155/2024/6652037","url":null,"abstract":"In this paper, integer- and fractional-order models are discussed to investigate the dynamics of malaria in a human host with a varied age distribution. A system of differential equation model with five human state variables and two mosquito state variables was examined. Preschool-age (0–5) and young-age individuals make up our model’s division of the human population. We investigated the existence of an area in which the model is both mathematically and epidemiologically well posed. According to the findings of our mathematical research, the disease-free equilibrium exists whenever the fundamental reproduction number <svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 13.1624 11.927\" width=\"13.1624pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"></path></g></svg> is smaller than one and is asymptotically stable. The disease-free equilibrium point is unstable when <span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 24.295 11.927\" width=\"24.295pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-83\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.664,0)\"></path></g></svg><span></span><span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"27.8771838 -8.6359 6.422 11.927\" width=\"6.422pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,27.927,0)\"></path></g></svg>.</span></span> We showed that the endemic equilibrium point is unique for <span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 24.295 11.927\" width=\"24.295pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-83\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.664,0)\"><use xlink:href=\"#g117-92\"></use></g></svg><span></span><span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"27.8771838 -8.6359 6.422 11.927\" width=\"6.422pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,27.927,0)\"><use xlink:href=\"#g113-50\"></use></g></svg>.</span></span> Also, the most influential control parameters of the spread of malaria were identified. Numerical simulations of both classical and fractional order were conducted, and we used ODE (45) for classical part and numerical technique developed by Toufik and Atangana for fractional order. The infected population ","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139396392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We first explore conditions under which every weighted composition-differentiation operator on the Hardy space is completely continuous. We then discuss necessary and sufficient conditions for these operators to be Hilbert–Schmidt on the derivative Hardy space .
{"title":"Composition-Differentiation Operators on Derivative Hardy Spaces","authors":"A. Abkar, A. Babaei","doi":"10.1155/2024/8222237","DOIUrl":"https://doi.org/10.1155/2024/8222237","url":null,"abstract":"We first explore conditions under which every weighted composition-differentiation operator on the Hardy space <svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 34.4579 13.8595\" width=\"34.4579pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,10.923,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.87,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.368,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.754,0)\"></path></g></svg> is completely continuous. We then discuss necessary and sufficient conditions for these operators to be Hilbert–Schmidt on the derivative Hardy space <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 29.656 13.8595\" width=\"29.656pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,6.136,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.083,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,15.581,0)\"><use xlink:href=\"#g197-15\"></use></g><g transform=\"matrix(.013,0,0,-0.013,24.967,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span>","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Moreen Brenda Gatwiri, Marilyn Ronoh, Cyrus Gitonga Ngari, Dominic Makaa Kitavi
Several pest management programs have been developed to control rising agricultural pest populations. However, the challenge of rapid evolution and pest resistance towards control measures continues to cause high production losses to maize farmers in Africa. Few models have attempted to address the issue of fall armyworm (FAW) but have barely incorporated the effect of insecticide resistance. Models with resistance would help predict the dynamics of the FAW population, thus mitigating losses. The main objectives of this work were to develop, analyze, and numerically simulate a susceptible-infected deterministic mathematical model expressing the FAW-maize interaction and population dynamics under insecticidal sprays and resistance FAW larvae. Three model steady states are established. Their local stability is conducted using either the eigenvalue or the Routh–Hurwitz stability criteria, and their global stability is analyzed using either the Castillo–Chavez, Perron eigenvector, or the Lyapunov methods. An expression for the basic reproduction number , together with the sensitivity analysis of its parameter values, is provided. Numerical analysis is conducted on various model parameter values. The results established all the model steady states to be locally and globally asymptotically stable at . Also, resistance increased the infection rates by increasing the FAW larvae survival rate
{"title":"Mathematical Modelling of Host-Pest Interaction in the Presence of Insecticides and Resistance: A Case of Fall Armyworm","authors":"Moreen Brenda Gatwiri, Marilyn Ronoh, Cyrus Gitonga Ngari, Dominic Makaa Kitavi","doi":"10.1155/2024/2886786","DOIUrl":"https://doi.org/10.1155/2024/2886786","url":null,"abstract":"Several pest management programs have been developed to control rising agricultural pest populations. However, the challenge of rapid evolution and pest resistance towards control measures continues to cause high production losses to maize farmers in Africa. Few models have attempted to address the issue of fall armyworm (FAW) but have barely incorporated the effect of insecticide resistance. Models with resistance would help predict the dynamics of the FAW population, thus mitigating losses. The main objectives of this work were to develop, analyze, and numerically simulate a susceptible-infected deterministic mathematical model expressing the FAW-maize interaction and population dynamics under insecticidal sprays and resistance FAW larvae. Three model steady states are established. Their local stability is conducted using either the eigenvalue or the Routh–Hurwitz stability criteria, and their global stability is analyzed using either the Castillo–Chavez, Perron eigenvector, or the Lyapunov methods. An expression for the basic reproduction number <span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 13.1624 11.927\" width=\"13.1624pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"></path></g></svg>,</span> together with the sensitivity analysis of its parameter values, is provided. Numerical analysis is conducted on various model parameter values. The results established all the model steady states to be locally and globally asymptotically stable at <span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 24.295 11.927\" width=\"24.295pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-83\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.664,0)\"></path></g></svg><span></span><span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"27.8771838 -8.6359 6.422 11.927\" width=\"6.422pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,27.927,0)\"></path></g></svg>.</span></span> Also, resistance <svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 8.42472 6.1673\" width=\"8.42472pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> increased the infection rates by increasing the FAW larvae survival rate <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 7.30254 9.49473\" width=\"7.30254pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlin","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we address the challenge of solving the nonlinear fractional Burger’s KdV equation, time-fractional Burger’s equation, and the fractional modified Burger’s equation. This is achieved by employing the Caputo and conformable derivatives. To tackle these equations, we introduce a new numerical method which is the combination of the local fractional Mohand transform and the Adomian decomposition method. This choice is driven by its straightforward methodology and reduced computational complexity. Moreover, to demonstrate the versatility of this technique, we provide several illustrative examples along with their corresponding exact or approximate solutions. These solutions are accompanied by graphical representations, further enhancing the clarity of the presented approach.
{"title":"New Local Fractional Mohand–Adomian Decomposition Method for Solving Nonlinear Fractional Burger’s Type Equation","authors":"Ihtisham Ul Haq, Ali Akgül, Zahid Ullah","doi":"10.1155/2024/1005771","DOIUrl":"https://doi.org/10.1155/2024/1005771","url":null,"abstract":"In this article, we address the challenge of solving the nonlinear fractional Burger’s KdV equation, time-fractional Burger’s equation, and the fractional modified Burger’s equation. This is achieved by employing the Caputo and conformable derivatives. To tackle these equations, we introduce a new numerical method which is the combination of the local fractional Mohand transform and the Adomian decomposition method. This choice is driven by its straightforward methodology and reduced computational complexity. Moreover, to demonstrate the versatility of this technique, we provide several illustrative examples along with their corresponding exact or approximate solutions. These solutions are accompanied by graphical representations, further enhancing the clarity of the presented approach.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139082180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than the actual market prices in the financial market. In order to change this situation, considering that the price change of the underlying is regarded as a fractal transmission system, the fractal derivative is introduced into the bond-pricing equation. In order to solve the fractal bond-pricing equation, we first convert it into an equivalent equation by using a fractal two-scale transform. Only in this case can we start to study it by means of the Lie symmetry analysis method. Then the geometric vector fields, the symmetry reductions, and the exact solution to the equations are obtained. Furthermore, the dynamic behaviors of the fractal bond-pricing equation are discussed. The results show that the fractal dimension bond-pricing formula can better explain price changes in the capital market than the classical one. That is to say, the classical bond-pricing equation is only a special case of the fractal-bond pricing equation, which makes up for the defect that the theoretical bond price given by the classical bond-pricing equation is often lower than the actual market price. The results of this paper provide a basis for bond pricing in the financial market in order to seek a more appropriate and real price.
{"title":"Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance","authors":"Chao Yue, Chuanhe Shen","doi":"10.1155/2024/9926131","DOIUrl":"https://doi.org/10.1155/2024/9926131","url":null,"abstract":"The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than the actual market prices in the financial market. In order to change this situation, considering that the price change of the underlying is regarded as a fractal transmission system, the fractal derivative is introduced into the bond-pricing equation. In order to solve the fractal bond-pricing equation, we first convert it into an equivalent equation by using a fractal two-scale transform. Only in this case can we start to study it by means of the Lie symmetry analysis method. Then the geometric vector fields, the symmetry reductions, and the exact solution to the equations are obtained. Furthermore, the dynamic behaviors of the fractal bond-pricing equation are discussed. The results show that the fractal dimension bond-pricing formula can better explain price changes in the capital market than the classical one. That is to say, the classical bond-pricing equation is only a special case of the fractal-bond pricing equation, which makes up for the defect that the theoretical bond price given by the classical bond-pricing equation is often lower than the actual market price. The results of this paper provide a basis for bond pricing in the financial market in order to seek a more appropriate and real price.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139082337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Syed Ahtsham Ul Haq Bokhary, Pakeeza Bashir, Allah Nawaz, Shreefa O. Hilali, Mohammed Alhagyan, Ameni Gargouri, Mohammed M. A. Almazah
Nanostar dendrimers are tree-like nanostructures with a well-defined, symmetrical architecture. They are built in a step-by-step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell. A weighted graph is a type of graph in which vertices or edges are assigned weights that represent cost, distance, and a variety of other relative measuring units. The weighted graphs have many applications and properties in a mathematical context. The topological indices are numerical values that represent the symmetry of a molecular structure. They have rich applications in theoretical chemistry. Various topological indices can be used to investigate a wide range of properties of chemical compounds with a molecular structure. They are very important in mathematical chemistry, especially in quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies. In this paper, we examine the topological properties of the molecular graphs of nanostar dendrimers. For this purpose, the topological indices, namely, the Wiener index and the Wiener polarity index are computed for a class of nanostar dendrimers.
{"title":"Computation of Wiener and Wiener Polarity Indices of a Class of Nanostar Dendrimer Using Vertex Weighted Graphs","authors":"Syed Ahtsham Ul Haq Bokhary, Pakeeza Bashir, Allah Nawaz, Shreefa O. Hilali, Mohammed Alhagyan, Ameni Gargouri, Mohammed M. A. Almazah","doi":"10.1155/2024/9941949","DOIUrl":"https://doi.org/10.1155/2024/9941949","url":null,"abstract":"Nanostar dendrimers are tree-like nanostructures with a well-defined, symmetrical architecture. They are built in a step-by-step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell. A weighted graph is a type of graph in which vertices or edges are assigned weights that represent cost, distance, and a variety of other relative measuring units. The weighted graphs have many applications and properties in a mathematical context. The topological indices are numerical values that represent the symmetry of a molecular structure. They have rich applications in theoretical chemistry. Various topological indices can be used to investigate a wide range of properties of chemical compounds with a molecular structure. They are very important in mathematical chemistry, especially in quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies. In this paper, we examine the topological properties of the molecular graphs of nanostar dendrimers. For this purpose, the topological indices, namely, the Wiener index and the Wiener polarity index are computed for a class of nanostar dendrimers.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139079555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammad Ayman-Mursaleen, Nadeem Rao, Mamta Rani, Adem Kilicman, Ahmed Ahmed Hussin Ali Al-Abied, Pradeep Malik
The objective of this paper is to construct univariate and bivariate blending type -Schurer–Kantorovich operators depending on two parameters and to approximate a class of measurable functions on
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