C. S. V. Varun Bose, R. Udhayakumar, V. Muthukumaran, S. Al-Omari
In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.
{"title":"A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects","authors":"C. S. V. Varun Bose, R. Udhayakumar, V. Muthukumaran, S. Al-Omari","doi":"10.37256/cm.5120243539","DOIUrl":"https://doi.org/10.37256/cm.5120243539","url":null,"abstract":"In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"4 4","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139383118","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}
Yohanes Leonardus Sukestiyarno, D. Wiyanti, Lathifatul Azizah, Wahyu Widada
Fluctuating stock prices make it difficult for investors to see investment opportunities. One tool that can help investors overcome this is represented by forecasting techniques. Long Short-Term Memory (LSTM) is one of deep learning methods used in forecasting time series. The training and success of deep learning is strongly influenced by the selection of hyperparameters. This research uses a hybrid method between the Genetic Algorithm (GA) and LSTM to find a suitable model for predicting stock prices. GA is used in optimizing the architecture such as the number of epochs, window size, and the number of LSTM units in the hidden layer. Tuning optimizer is also carried out using several optimizers to achieve the best value. From method that has been applied, it shows that the method has a good level of accuracy with MAPE values below 10% in every optimizer used. The error rate generated is quite low, in case-1 with a minimum RMSE value of 93.03 and 94.40, & in case-2 with an RMSE value of 104.99 and 150.06 during training and testing. A fairly stable and small value is generated by setting it using the Adam Optimizer.
{"title":"Algorithm Optimizer in GA-LSTM for Stock Price Forecasting","authors":"Yohanes Leonardus Sukestiyarno, D. Wiyanti, Lathifatul Azizah, Wahyu Widada","doi":"10.37256/cm.5120243367","DOIUrl":"https://doi.org/10.37256/cm.5120243367","url":null,"abstract":"Fluctuating stock prices make it difficult for investors to see investment opportunities. One tool that can help investors overcome this is represented by forecasting techniques. Long Short-Term Memory (LSTM) is one of deep learning methods used in forecasting time series. The training and success of deep learning is strongly influenced by the selection of hyperparameters. This research uses a hybrid method between the Genetic Algorithm (GA) and LSTM to find a suitable model for predicting stock prices. GA is used in optimizing the architecture such as the number of epochs, window size, and the number of LSTM units in the hidden layer. Tuning optimizer is also carried out using several optimizers to achieve the best value. From method that has been applied, it shows that the method has a good level of accuracy with MAPE values below 10% in every optimizer used. The error rate generated is quite low, in case-1 with a minimum RMSE value of 93.03 and 94.40, & in case-2 with an RMSE value of 104.99 and 150.06 during training and testing. A fairly stable and small value is generated by setting it using the Adam Optimizer.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"55 17","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139382103","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, Hilfer fractional differential equation is studied. Firstly, we used Laplace transform and semigroup theory to find the mild solution of the system. Then exact controllability of proposed system is established using the Arzela-Ascoli theorem and Schauder fixed point theorem. To illustrate the developed theory we provide an example at the end.
{"title":"Controllability of Hilfer Fractional Semilinear Integro-Differential Equation of Order α ∊ (0, 1), β ∊ [0, 1]","authors":"Vidushi Tripathi, Sanjukta Das","doi":"10.37256/cm.5120242526","DOIUrl":"https://doi.org/10.37256/cm.5120242526","url":null,"abstract":"In this paper, Hilfer fractional differential equation is studied. Firstly, we used Laplace transform and semigroup theory to find the mild solution of the system. Then exact controllability of proposed system is established using the Arzela-Ascoli theorem and Schauder fixed point theorem. To illustrate the developed theory we provide an example at the end.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"10 24","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139382931","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}
Consider q to be an integer, and χ to be a Dirichlet character (mod q). The main purpose of this paper is using the analytic methods to study some problems related to the Dirichlet character (mod q).
{"title":"A Study of Some Problems on the Dirichlet Characters (mod q)","authors":"A. Hakami","doi":"10.37256/cm.5120243467","DOIUrl":"https://doi.org/10.37256/cm.5120243467","url":null,"abstract":"Consider q to be an integer, and χ to be a Dirichlet character (mod q). The main purpose of this paper is using the analytic methods to study some problems related to the Dirichlet character (mod q).","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"2 6","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139389670","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}
A. G. Syarifudin, I. Muchtadi-Alamsyah, E. Suwastika
Let R be a commutative ring with identity, and P be a prime ideal of R. The prime ideal graph, denoted by Γp, is the graph where the set of vertices is R/{0} and two vertices are joined by an edge if their product belongs to P. This paper will discuss topological indices and some properties of the prime ideal graph of a commutative ring and its line graph. Topological indices, such as the Wiener, first Zagreb, second Zagreb, Harary, Gutman, Schultz, and Harmonic indices, are related to the degree of vertices and the diameter of the graphs. In this paper, we also discuss the independence and domination numbers of the line graph.
{"title":"Topological Indices and Properties of the Prime Ideal Graph of a Commutative Ring and Its Line Graph","authors":"A. G. Syarifudin, I. Muchtadi-Alamsyah, E. Suwastika","doi":"10.37256/cm.5120243574","DOIUrl":"https://doi.org/10.37256/cm.5120243574","url":null,"abstract":"Let R be a commutative ring with identity, and P be a prime ideal of R. The prime ideal graph, denoted by Γp, is the graph where the set of vertices is R/{0} and two vertices are joined by an edge if their product belongs to P. This paper will discuss topological indices and some properties of the prime ideal graph of a commutative ring and its line graph. Topological indices, such as the Wiener, first Zagreb, second Zagreb, Harary, Gutman, Schultz, and Harmonic indices, are related to the degree of vertices and the diameter of the graphs. In this paper, we also discuss the independence and domination numbers of the line graph.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"115 40","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139391227","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}
Kassifou Traore, Djideme F. Houenou, Romain Glèlè Kakaï
The COVID-19 pandemic was caused by the rapid spread of a new coronavirus (SARS-CoV-2) worldwide. COVID-19 pandemic mitigation measures caused significant social and economic disruption, especially in regions with weak economic and fragile healthcare systems like West Africa. Therefore, accurate knowledge of the impact of these measures on its dynamics is important in decision-making. In this study, we formulated and used a deterministic compartmental model, considering two sub-classes of susceptible individuals (S1 and S2), where S1 is the population living around the epicenter of the epidemic and S2 is the population living far from the epicenter of the epidemic. The aim was to (i) theoretically assess the impact of measures reducing the transmission rate of the disease (ψ) on the epidemic dynamics and (ii) analyze the impact of measures reducing the probability of contact between infected and susceptible individuals (detection and isolation rates, θap, θs) on the epidemic dynamics. We determined the expressions of the basic and control reproduction numbers and studied the sensitivity and elasticity of the control reproduction number with respect to ψ, θap, θs, and heterogeneity factor, k(S1/S2). Application to the COVID-19 first-wave data from West Africa revealed that the basic reproduction number was 1.85. Moreover, the results indicated that a 50% reduction in the transmission rate of COVID-19 or the detection and isolation of 10% of infected individuals per day should help to reach the peak of the epidemic. Furthermore, a 100% increase in the heterogeneity factor induces a 16% increase in the control reproduction number when θap = 0.15 and a 14% increase in the control reproduction number when θap = 0.6. These conclusions could help design control measures to curtail future epidemics.
{"title":"Analytical insights of the effects of Non-Pharmaceutical Interventions on SRAS-CoV-2 Dynamic with Application to West African Data","authors":"Kassifou Traore, Djideme F. Houenou, Romain Glèlè Kakaï","doi":"10.37256/cm.4420232868","DOIUrl":"https://doi.org/10.37256/cm.4420232868","url":null,"abstract":"The COVID-19 pandemic was caused by the rapid spread of a new coronavirus (SARS-CoV-2) worldwide. COVID-19 pandemic mitigation measures caused significant social and economic disruption, especially in regions with weak economic and fragile healthcare systems like West Africa. Therefore, accurate knowledge of the impact of these measures on its dynamics is important in decision-making. In this study, we formulated and used a deterministic compartmental model, considering two sub-classes of susceptible individuals (S1 and S2), where S1 is the population living around the epicenter of the epidemic and S2 is the population living far from the epicenter of the epidemic. The aim was to (i) theoretically assess the impact of measures reducing the transmission rate of the disease (ψ) on the epidemic dynamics and (ii) analyze the impact of measures reducing the probability of contact between infected and susceptible individuals (detection and isolation rates, θap, θs) on the epidemic dynamics. We determined the expressions of the basic and control reproduction numbers and studied the sensitivity and elasticity of the control reproduction number with respect to ψ, θap, θs, and heterogeneity factor, k(S1/S2). Application to the COVID-19 first-wave data from West Africa revealed that the basic reproduction number was 1.85. Moreover, the results indicated that a 50% reduction in the transmission rate of COVID-19 or the detection and isolation of 10% of infected individuals per day should help to reach the peak of the epidemic. Furthermore, a 100% increase in the heterogeneity factor induces a 16% increase in the control reproduction number when θap = 0.15 and a 14% increase in the control reproduction number when θap = 0.6. These conclusions could help design control measures to curtail future epidemics.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"89 11","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138954471","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}
Mukund Mohan, Abhimanyu Kumar, S. N. Roy, P. K. Parida
Real-world applications depend heavily on the fixed-point solution. In this paper, we have suggested an effective iterative method for fixed points. We have first given the approximate order of convergence for this method using Taylor’s series. The radii of convergence balls for this method can then be calculated using a local convergence theorem that we then present. The semilocal convergence theorem, which determines the starting point’s accuracy, is then presented. We have created some technical lemmas and theorems to serve this purpose. In contrast to an earlier study using the same type of method for nonlinear equations, we have not used the convergence conditions on higher-order Frechet derivatives in our study of convergence. Finally, some numerical examples are provided to support the theoretical findings we made. This highlights the uniqueness of this study.
{"title":"On an Efficient Iterative Method for Fixed Points","authors":"Mukund Mohan, Abhimanyu Kumar, S. N. Roy, P. K. Parida","doi":"10.37256/cm.4420232755","DOIUrl":"https://doi.org/10.37256/cm.4420232755","url":null,"abstract":"Real-world applications depend heavily on the fixed-point solution. In this paper, we have suggested an effective iterative method for fixed points. We have first given the approximate order of convergence for this method using Taylor’s series. The radii of convergence balls for this method can then be calculated using a local convergence theorem that we then present. The semilocal convergence theorem, which determines the starting point’s accuracy, is then presented. We have created some technical lemmas and theorems to serve this purpose. In contrast to an earlier study using the same type of method for nonlinear equations, we have not used the convergence conditions on higher-order Frechet derivatives in our study of convergence. Finally, some numerical examples are provided to support the theoretical findings we made. This highlights the uniqueness of this study.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 14","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138961593","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 investigated the dynamical behavior of a fuzzy mathematical model with tuberculosis (TB) treatment function. The considered model analyzes fuzzy basic reproduction numbers and stability analysis for both local and global stability conditions around disease-free equilibrium points, as well as its local stability conditions around endemic equilibrium points. We examine the TB model’s sensitivity analysis with a focus on the variation of each of its parameters. We propose predicting the extension of the virus load in TB using fuzzy bifurcation. At the end, we have given a numerical simulation to illustrate the outcomes by considering some special types of treatment functions.
{"title":"Analyzing Dynamical Behavior of Tuberculosis Transmission","authors":"P. Monisha, S. Sindu Devi","doi":"10.37256/cm.4420232621","DOIUrl":"https://doi.org/10.37256/cm.4420232621","url":null,"abstract":"In this article, we investigated the dynamical behavior of a fuzzy mathematical model with tuberculosis (TB) treatment function. The considered model analyzes fuzzy basic reproduction numbers and stability analysis for both local and global stability conditions around disease-free equilibrium points, as well as its local stability conditions around endemic equilibrium points. We examine the TB model’s sensitivity analysis with a focus on the variation of each of its parameters. We propose predicting the extension of the virus load in TB using fuzzy bifurcation. At the end, we have given a numerical simulation to illustrate the outcomes by considering some special types of treatment functions.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 6","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138962672","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 discuss the stochastic comparison of two classical surplus processes in an one-year insurance period. Under the Marshall-Olkin extended Weibull random aggregate claim amounts, we establish some sufficient conditions for the comparison of aggregate claim amounts in the sense of the usual stochastic order. Applications of our results to the Value-at-Risk and ruin probability are also given. The obtained results show that the heterogeneity of the risks in a given insurance portfolio tends to make the portfolio volatile, which in turn leads to requiring more capital. We also obtain some sufficient conditions for comparing aggregate non-random claim amounts with different occurrence frequency vectors in terms of increasing convex order.
{"title":"Ordering Results of Aggregate Claim Amounts from Two Heterogeneous Portfolios","authors":"S. K. Ramani, H. Jafari, G. Saadat, Kia Barmalzan","doi":"10.37256/cm.4420232494","DOIUrl":"https://doi.org/10.37256/cm.4420232494","url":null,"abstract":"In this paper, we discuss the stochastic comparison of two classical surplus processes in an one-year insurance period. Under the Marshall-Olkin extended Weibull random aggregate claim amounts, we establish some sufficient conditions for the comparison of aggregate claim amounts in the sense of the usual stochastic order. Applications of our results to the Value-at-Risk and ruin probability are also given. The obtained results show that the heterogeneity of the risks in a given insurance portfolio tends to make the portfolio volatile, which in turn leads to requiring more capital. We also obtain some sufficient conditions for comparing aggregate non-random claim amounts with different occurrence frequency vectors in terms of increasing convex order.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138963222","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}
Ming-Yue Wang, A. Biswas, Y. Yıldırım, A. Alshomrani
The present paper is a sequel to the paper on the topic with Kerr law nonlinearity. For power-law nonlinearity, it was derived through balancing principle that the solitons would exist for two values of the power-law parameter, namely n = 1 or n = 2. The current paper derives dark and singular solitons for the latter value of n since the first case was already covered in a previous report that was dedicated to address the model with Kerr law.
本文是有关克尔定律非线性的论文的续篇。对于幂律非线性，通过平衡原理推导出，孤子会在两个幂律参数值下存在，即 n = 1 或 n = 2。本文推导的是后一种 n 值的暗孤子和奇异孤子，因为前一种情况已在专门讨论具有克尔定律模型的前一份报告中涉及。
{"title":"Optical Solitons for the Dispersive Concatenation Model with Power-Law Nonlinearity by the Complete Discriminant Approach","authors":"Ming-Yue Wang, A. Biswas, Y. Yıldırım, A. Alshomrani","doi":"10.37256/cm.4420233814","DOIUrl":"https://doi.org/10.37256/cm.4420233814","url":null,"abstract":"The present paper is a sequel to the paper on the topic with Kerr law nonlinearity. For power-law nonlinearity, it was derived through balancing principle that the solitons would exist for two values of the power-law parameter, namely n = 1 or n = 2. The current paper derives dark and singular solitons for the latter value of n since the first case was already covered in a previous report that was dedicated to address the model with Kerr law.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 30","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138964505","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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