Iron oxide, Silver, Aluminium oxide, these nanoparticles individually or combined help in drug delivery especially aluminium oxide nanofluid used in an anti-blood pressure drug called 'Telmisartan'. Alumina and silver particles are used in manufacturing nanocomposites which have more antimicrobial properties. This is the reason for the current study of ternary nanofluids natural convective flow and efficacy of energy transfer in a bi-directionally sheet. Currently, ternary nanofluids (Fe3O4, Ag, Al2O3) are being taken for analysis. Usual water (H2O) is the conventional base fluid. Two different combinations of ternary nanofluids are used to get the average heat transfer rate, mixture ratios (Fe3O4 + Ag) and (Fe3O4 + Ag + Al2O3) when subjected to a variety of physical influences, including thermal radiation, magnetic fields, heat production and absorption, and nanoparticle volume amount. It is possible to solve the developed set of equations numerical results using the Keller box (finite differences) method with the help of MATLAB programming. This method helps in solving higher order partial differential equation (PDEs) to ordinary differential equation (ODEs). The investigations findings demonstrated that the ternary hybrid nanofluids specific heat capacity is directly impacted by temperature. Numerical solutions for Nusselt number, velocity profile, skin friction coefficient, temperature profiles have represented with the help of graphs and tables. The ternary hybrid nanoflow (Fe3O4 + Ag + Al2O3/H2O) transmits more energy for increasing volume fractions, comparing to the hybrid nanofluid (Fe3O4 + Ag/H2O). The study reveals the fact that metal oxides transfer more heat from the system than that of metals. The estimated error of heat transfer rate is higher in alumina nanoflow followed by silver and iron oxide nanofluid flows. The streamlines are equally spaced, but the energy flow amount is higher for the case M, S = 1 than M, S = 2. But in the case of stretching ratio parameter, the amount energy flow in α = 0.5 > α = 1.0. An equal amount of energy flow is observed for varied Biot number.
氧化铁、银、氧化铝，这些纳米粒子单独或组合在一起有助于药物输送，特别是氧化铝纳米流体用于一种名为 "替米沙坦 "的抗血压药物。氧化铝和银粒子用于制造纳米复合材料，具有更强的抗菌性能。这就是目前研究三元纳米流体在双向片中的自然对流和能量传递效率的原因。目前正在对三元纳米流体（Fe3O4、Ag、Al2O3）进行分析。水（H2O）是传统的基础流体。采用两种不同的三元纳米流体组合，得出在热辐射、磁场、产热和吸热以及纳米粒子体积量等各种物理影响下的平均传热率、混合比（Fe3O4 + Ag）和（Fe3O4 + Ag + Al2O3）。在 MATLAB 编程的帮助下，可以使用 Keller box（有限差分）方法求解所开发的方程组数值结果。这种方法有助于从高阶偏微分方程（PDE）到常微分方程（ODE）的求解。研究结果表明，三元混合纳米流体的比热容直接受温度影响。努塞尔特数、速度曲线、表皮摩擦系数和温度曲线的数值解都借助图表来表示。与混合纳米流体（Fe3O4 + Ag/H2O）相比，三元混合纳米流体（Fe3O4 + Ag + Al2O3/H2O）在体积分数增加时传输更多能量。研究表明，金属氧化物比金属氧化物从系统中传递更多的热量。氧化铝纳米流体的传热率估计误差较大，其次是银纳米流体和氧化铁纳米流体。流线间距相等，但 M, S = 1 情况下的能量流量高于 M, S = 2。但在拉伸比参数的情况下，α = 0.5 时的能量流大于α = 1.0 时的能量流。在不同的 Biot 数下，观察到的能量流数量相同。
{"title":"Computational Approach on Convective-Magneto Trihybrid Nanoflow with Space Dependent Energy Source/Sink: Drug Delivery","authors":"B. Vinothkumar, T. Poornima","doi":"10.37256/cm.5120244056","DOIUrl":"https://doi.org/10.37256/cm.5120244056","url":null,"abstract":"Iron oxide, Silver, Aluminium oxide, these nanoparticles individually or combined help in drug delivery especially aluminium oxide nanofluid used in an anti-blood pressure drug called 'Telmisartan'. Alumina and silver particles are used in manufacturing nanocomposites which have more antimicrobial properties. This is the reason for the current study of ternary nanofluids natural convective flow and efficacy of energy transfer in a bi-directionally sheet. Currently, ternary nanofluids (Fe3O4, Ag, Al2O3) are being taken for analysis. Usual water (H2O) is the conventional base fluid. Two different combinations of ternary nanofluids are used to get the average heat transfer rate, mixture ratios (Fe3O4 + Ag) and (Fe3O4 + Ag + Al2O3) when subjected to a variety of physical influences, including thermal radiation, magnetic fields, heat production and absorption, and nanoparticle volume amount. It is possible to solve the developed set of equations numerical results using the Keller box (finite differences) method with the help of MATLAB programming. This method helps in solving higher order partial differential equation (PDEs) to ordinary differential equation (ODEs). The investigations findings demonstrated that the ternary hybrid nanofluids specific heat capacity is directly impacted by temperature. Numerical solutions for Nusselt number, velocity profile, skin friction coefficient, temperature profiles have represented with the help of graphs and tables. The ternary hybrid nanoflow (Fe3O4 + Ag + Al2O3/H2O) transmits more energy for increasing volume fractions, comparing to the hybrid nanofluid (Fe3O4 + Ag/H2O). The study reveals the fact that metal oxides transfer more heat from the system than that of metals. The estimated error of heat transfer rate is higher in alumina nanoflow followed by silver and iron oxide nanofluid flows. The streamlines are equally spaced, but the energy flow amount is higher for the case M, S = 1 than M, S = 2. But in the case of stretching ratio parameter, the amount energy flow in α = 0.5 > α = 1.0. An equal amount of energy flow is observed for varied Biot number.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140252441","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 the present article, we establish sufficient conditions for the existence of a unique bounded solution using a prominent fixed-point theorem for the non-linear initial value problem involving the recently introduced Hilfer nabla fractional difference operator. where 0 <ℵ<1, 0 ≤ ß ≤1, ι =ℵ+ ß −ℵß and j : Nx × Rn →Rn. We also analyze the Ulam-Hyers stability of the considered problem and make some interesting observations on the dependence of its solutions on initial conditions and parameters. Finally, we conclude this article by constructing suitable examples to illustrate the applicability of established results.
{"title":"Data Dependence and Existence and Uniqueness for Hilfer Nabla Fractional Difference Equations","authors":"N. S. Gopal, Jagan Mohan Jonnalagadda, J. Alzabut","doi":"10.37256/cm.5120242552","DOIUrl":"https://doi.org/10.37256/cm.5120242552","url":null,"abstract":"In the present article, we establish sufficient conditions for the existence of a unique bounded solution using a prominent fixed-point theorem for the non-linear initial value problem involving the recently introduced Hilfer nabla fractional difference operator.\u0000\u0000where 0 <ℵ<1, 0 ≤ ß ≤1, ι =ℵ+ ß −ℵß and j : Nx × Rn →Rn. We also analyze the Ulam-Hyers stability of the considered problem and make some interesting observations on the dependence of its solutions on initial conditions and parameters. Finally, we conclude this article by constructing suitable examples to illustrate the applicability of established results.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140257183","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}
T. Sreenivasula Reddy, R. Sathya, Mallikhanjuna Rao Nuka
Recent years have seen a lot of attention paid to the mining of enormous item sets from high-dimensional databases. Small and mid-sized data sets take a long time to mine with traditional algorithms since they don’t include the complete and relevant info needed for decision making. Many applications, particularly in bioinformatics, benefit greatly from the extraction of (FCCI) Frequent Colossal Closed Itemsets from a large dataset. In order to extract FCCI from a dataset, present preprocessing strategies fail to remove all extraneous characteristics and rows from the data set completely. In addition, the most current algorithms for this kind are sequential and computationally expensive. A high-dimensional dataset is pruned of all extraneous characteristics and rows using two alternative dimensionality reduction strategies presented in this paper. Then, an optimal feature value is identified by using Equilibrium Optimizer (EO) to identify the threshold value for reduced features. It is designed to discover common items and build association rules if the feature value is smaller than the frequency mining algorithm (IFRS) in conjunction with the Fruit fly Algorithm (FFA). If the feature value exceeds the optimal threshold, then optimized Length restrictions can be used to solve the CP mining problem (LC). Random search is utilized to identify the optimal threshold values of the restrictions and extract the enormous pattern using the Differential Evolutionary Arithmetic Optimization Algorithm. The experiments are carried on twenty biological datasets that us extracted from UCI websites and validated the proposed models in terms of various metrics.
{"title":"Mining the High Dimensional Biological Dataset Using Optimized Colossal Pattern with Dimensionality Reduction","authors":"T. Sreenivasula Reddy, R. Sathya, Mallikhanjuna Rao Nuka","doi":"10.37256/cm.5120242460","DOIUrl":"https://doi.org/10.37256/cm.5120242460","url":null,"abstract":"Recent years have seen a lot of attention paid to the mining of enormous item sets from high-dimensional databases. Small and mid-sized data sets take a long time to mine with traditional algorithms since they don’t include the complete and relevant info needed for decision making. Many applications, particularly in bioinformatics, benefit greatly from the extraction of (FCCI) Frequent Colossal Closed Itemsets from a large dataset. In order to extract FCCI from a dataset, present preprocessing strategies fail to remove all extraneous characteristics and rows from the data set completely. In addition, the most current algorithms for this kind are sequential and computationally expensive. A high-dimensional dataset is pruned of all extraneous characteristics and rows using two alternative dimensionality reduction strategies presented in this paper. Then, an optimal feature value is identified by using Equilibrium Optimizer (EO) to identify the threshold value for reduced features. It is designed to discover common items and build association rules if the feature value is smaller than the frequency mining algorithm (IFRS) in conjunction with the Fruit fly Algorithm (FFA). If the feature value exceeds the optimal threshold, then optimized Length restrictions can be used to solve the CP mining problem (LC). Random search is utilized to identify the optimal threshold values of the restrictions and extract the enormous pattern using the Differential Evolutionary Arithmetic Optimization Algorithm. The experiments are carried on twenty biological datasets that us extracted from UCI websites and validated the proposed models in terms of various metrics.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140256938","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}
Mahboobeh Zakeri, Abbas Sahleh, H. Lakzian, Vladimir Rakočević
The aim of this paper is to generalize Caristi’s theorem, Bollenbacher and Hicks’ theorem, and also Hicks and Rhoades’ theorem by substituting the continuity assumption with relatively weaker conditions of k-continuity or (C; k) condition in a complete metric space with a w-distance. Another proof for Caristi’s theorem using Zorn’s lemma will be given. Some examples will confirm the novelty and usefulness of our results.
本文的目的是在具有 w 距离的完全度量空间中，用相对较弱的 k 连续性条件或 (C; k) 条件替代连续性假设，从而推广卡利斯蒂定理、波伦巴赫和希克斯定理以及希克斯和罗兹定理。还将给出另一个使用佐恩（Zorn）定理的卡利斯提定理证明。一些实例将证实我们的结果的新颖性和实用性。
{"title":"Caristi-Type Fixed-Point Theorems in the Framework w-Distances","authors":"Mahboobeh Zakeri, Abbas Sahleh, H. Lakzian, Vladimir Rakočević","doi":"10.37256/cm.5120242584","DOIUrl":"https://doi.org/10.37256/cm.5120242584","url":null,"abstract":"The aim of this paper is to generalize Caristi’s theorem, Bollenbacher and Hicks’ theorem, and also Hicks and Rhoades’ theorem by substituting the continuity assumption with relatively weaker conditions of k-continuity or (C; k) condition in a complete metric space with a w-distance. Another proof for Caristi’s theorem using Zorn’s lemma will be given. Some examples will confirm the novelty and usefulness of our results.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140256886","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 are proposing an updated form of Krylov subspace-based interpolatory projection techniques for the stabilization of incompressible Navier-Stokes flows. In the proposed techniques, we utilize the reduced-order modelling approach implicitly, where reduced-order matrices need not be gathered explicitly. To estimate the aimed optimal feedback matrix, only the factored solution of the desired continuous-time algebraic Riccati equation (CARE) needs to be stored through the classical eigenvalue decomposition. The sparse structure of the target systems will remain invariant within the matrix-vector operations for generating the bases of the projector matrices through Krylov subspace techniques, where a cohesive projection scheme will be incorporated to ensure the potency of the projector matrices. So, the proposed techniques will be feasible for memory allocation and enhance the rapid convergence of the simulation. Analysis of the target systems’ transient characteristics, such as eigenvalues and step-responses, will be used to ascertain the competence and reliability of the proposed techniques. Necessary computation will be done numerically through MATLAB. Stabilization of the transient behaviors and minimization of the simulation time are the prime concerns in this work. Eventually, by comparing with the contemporary techniques the advancement of the proposed techniques will be confirmed.
{"title":"Memory-Efficient Interpolatory Projection Techniques for the Stabilization of Incompressible Navier-Stokes Flows","authors":"M. Uddin, M. Uddin, Md. Abdul, Hakim Khan","doi":"10.37256/cm.5120243646","DOIUrl":"https://doi.org/10.37256/cm.5120243646","url":null,"abstract":"In this article, we are proposing an updated form of Krylov subspace-based interpolatory projection techniques for the stabilization of incompressible Navier-Stokes flows. In the proposed techniques, we utilize the reduced-order modelling approach implicitly, where reduced-order matrices need not be gathered explicitly. To estimate the aimed optimal feedback matrix, only the factored solution of the desired continuous-time algebraic Riccati equation (CARE) needs to be stored through the classical eigenvalue decomposition. The sparse structure of the target systems will remain invariant within the matrix-vector operations for generating the bases of the projector matrices through Krylov subspace techniques, where a cohesive projection scheme will be incorporated to ensure the potency of the projector matrices. So, the proposed techniques will be feasible for memory allocation and enhance the rapid convergence of the simulation. Analysis of the target systems’ transient characteristics, such as eigenvalues and step-responses, will be used to ascertain the competence and reliability of the proposed techniques. Necessary computation will be done numerically through MATLAB. Stabilization of the transient behaviors and minimization of the simulation time are the prime concerns in this work. Eventually, by comparing with the contemporary techniques the advancement of the proposed techniques will be confirmed.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140266187","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 investigate the behaviors of the measles viral pandemic using fuzzy susceptible-infectiousrecovered (SIR) model. To examine the effects of various compartment phases, we analyze disease-free equilibrium points along with basic reproduction number. The measles model is stated to be globally asymptotically stable at the disease-free equilibrium point. In order to mathematically simulate the measles, we use a first-order nonlinear differential equation. The numerical solution is computed using the Runge-Kutta method, and the model’s feasibility is also covered.
{"title":"Feasibility and Stability Analysis for Basic Measles Model Using Fuzzy Parameter","authors":"H. A. Bhavithra, S. Sindu Devi","doi":"10.37256/cm.5120242428","DOIUrl":"https://doi.org/10.37256/cm.5120242428","url":null,"abstract":"In this article, we investigate the behaviors of the measles viral pandemic using fuzzy susceptible-infectiousrecovered (SIR) model. To examine the effects of various compartment phases, we analyze disease-free equilibrium points along with basic reproduction number. The measles model is stated to be globally asymptotically stable at the disease-free equilibrium point. In order to mathematically simulate the measles, we use a first-order nonlinear differential equation. The numerical solution is computed using the Runge-Kutta method, and the model’s feasibility is also covered.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140448904","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}
Abstract: In this model, the manufacturer needs to inspect and rework defective items due to the flawed manufacturing process. When checking for defective products, two types of errors, namely Type 1 error and Type 2 error, may occur at the inspection stage. If a lot of defective materials are rejected during the inspection, a non-destructive screening process separates the material into reworkable and non-defective categories. This study includes inspection rate insufficiency (IRI) and inspection rate sufficiency (IRS) based on the relationship between inspection and production rates. Rework Priority Policy (RPP) is followed in every scenario. This paper aims to minimize the inspection error and optimize the total profit. Numerical examples help demonstrate the value of this well-established model. A sensitivity analysis of this study was carried out to check its accuracy.
{"title":"Impact of Inspection Error of an Economic Production Quantity Model with Acceptance Sampling, Defective Items, and Rework","authors":"Palanivel M, Venkadesh M","doi":"10.37256/cm.5120242426","DOIUrl":"https://doi.org/10.37256/cm.5120242426","url":null,"abstract":"Abstract: In this model, the manufacturer needs to inspect and rework defective items due to the flawed manufacturing process. When checking for defective products, two types of errors, namely Type 1 error and Type 2 error, may occur at the inspection stage. If a lot of defective materials are rejected during the inspection, a non-destructive screening process separates the material into reworkable and non-defective categories. This study includes inspection rate insufficiency (IRI) and inspection rate sufficiency (IRS) based on the relationship between inspection and production rates. Rework Priority Policy (RPP) is followed in every scenario. This paper aims to minimize the inspection error and optimize the total profit. Numerical examples help demonstrate the value of this well-established model. A sensitivity analysis of this study was carried out to check its accuracy.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140446685","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 will introduce a well-known transformation technique, the modified α-fractional differential transform, to the differential equation of fractional order. We derive some new results with proof using new techniques that never existed before. By using this new technique, we are attempting to solve the nonlinear fractional-order mathematical epidemic model. Furthermore, the fractional epidemic model’s solution obtained by using this new technique is correlated with the solution of the same model calculated for a different fractional order by the modified α-fractional differential transform method. Moreover, using the Python software, we can numerically and graphically represent the solution of fractional differential equations.
{"title":"Simulation of Fractional Order 2D-Mathematical Model Using α-Fractional Differential Transform Method","authors":"S. N. Thorat, K. P. Ghadle, R. Muneshwar","doi":"10.37256/cm.5120242464","DOIUrl":"https://doi.org/10.37256/cm.5120242464","url":null,"abstract":"In this paper, we will introduce a well-known transformation technique, the modified α-fractional differential transform, to the differential equation of fractional order. We derive some new results with proof using new techniques that never existed before. By using this new technique, we are attempting to solve the nonlinear fractional-order mathematical epidemic model. Furthermore, the fractional epidemic model’s solution obtained by using this new technique is correlated with the solution of the same model calculated for a different fractional order by the modified α-fractional differential transform method. Moreover, using the Python software, we can numerically and graphically represent the solution of fractional differential equations.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140447734","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}
From this present study, derive the two consecutive demands between the time intervals: economic order quantity and total annual variable cost. The solution for this inventory model is optimizing the total annual variable cost. Here, given an arithmetical example and sensitivity analysis for the provision of the inventory model, assume the planning horizon and replenishment rate are infinite. To the best of our knowledge, this is the first study to find out the total annual variable cost using various costs under the condition of a permissible delay in payments with an allowed stock-out cost and lead time.
{"title":"An EOQ Model Under the Condition of Permissible Delay in Payments with Allowed Stock-Out Cost and Lead Time","authors":"Jayanthi J","doi":"10.37256/cm.5120242462","DOIUrl":"https://doi.org/10.37256/cm.5120242462","url":null,"abstract":"From this present study, derive the two consecutive demands between the time intervals: economic order quantity and total annual variable cost. The solution for this inventory model is optimizing the total annual variable cost. Here, given an arithmetical example and sensitivity analysis for the provision of the inventory model, assume the planning horizon and replenishment rate are infinite. To the best of our knowledge, this is the first study to find out the total annual variable cost using various costs under the condition of a permissible delay in payments with an allowed stock-out cost and lead time.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140448433","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 study investigates the logistic model of a single species incorporating the additive Allee effect using Caputo fractional order differential equations. The Allee effect describes a positive correlation between individual fitness and population density at low densities. Populations subjected to the strong Allee effect can move towards extinction when their population is below a critical level. This study calculates the threshold level of the population suffering from the strong Allee effect. Various published studies are showing that fractional order models are more appropriate for explaining real-world phenomena than ordinary integer-order systems; therefore, this study involves the use of the Caputo fractional order derivative. Single-species models have been extensively used in mathematical biology, such as insect control, optimal biological resource planning, epidemic avoidance and control, and cell growth regulation. This study can help save vulnerable species from extinction and eliminate unwanted species by subjecting them to a strong Allee effect using artificial strategies.
{"title":"Modeling and Analysis of Fractional Order Logistic Equation Incorporating Additive Allee Effect","authors":"Preety Kalra, Nisha Malhotra","doi":"10.37256/cm.5120243183","DOIUrl":"https://doi.org/10.37256/cm.5120243183","url":null,"abstract":"This study investigates the logistic model of a single species incorporating the additive Allee effect using Caputo fractional order differential equations. The Allee effect describes a positive correlation between individual fitness and population density at low densities. Populations subjected to the strong Allee effect can move towards extinction when their population is below a critical level. This study calculates the threshold level of the population suffering from the strong Allee effect. Various published studies are showing that fractional order models are more appropriate for explaining real-world phenomena than ordinary integer-order systems; therefore, this study involves the use of the Caputo fractional order derivative. Single-species models have been extensively used in mathematical biology, such as insect control, optimal biological resource planning, epidemic avoidance and control, and cell growth regulation. This study can help save vulnerable species from extinction and eliminate unwanted species by subjecting them to a strong Allee effect using artificial strategies.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140492361","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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