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Stability analysis of fractional order modelling of social media addiction 社交媒体成瘾分数阶模型的稳定性分析
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022040
Pradeep Malik, Deepika
{"title":"Stability analysis of fractional order modelling of social media addiction","authors":"Pradeep Malik, Deepika","doi":"10.3934/mfc.2022040","DOIUrl":"https://doi.org/10.3934/mfc.2022040","url":null,"abstract":"<p style='text-indent:20px;'>In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point <inline-formula><tex-math id=\"M1\">begin{document}$ E_{0} $end{document}</tex-math></inline-formula>, endemic equilibrium point <inline-formula><tex-math id=\"M2\">begin{document}$ E_{*} $end{document}</tex-math></inline-formula>, and basic reproduction number <inline-formula><tex-math id=\"M3\">begin{document}$ R_0 $end{document}</tex-math></inline-formula> have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"6 1","pages":"670-690"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70219010","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}
引用次数: 0
Optimal investment strategy for the DC pension plan based on jump diffusion model and S-shaped utility 基于跳跃扩散模型和s型效用的DC养老金计划最优投资策略
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023007
Jiaxin Lu, Hua Dong
{"title":"Optimal investment strategy for the DC pension plan based on jump diffusion model and S-shaped utility","authors":"Jiaxin Lu, Hua Dong","doi":"10.3934/mfc.2023007","DOIUrl":"https://doi.org/10.3934/mfc.2023007","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220333","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}
引用次数: 0
Study on the well-posedness of stochastic Boussinesq equations with Navier boundary conditions 具有Navier边界条件的随机Boussinesq方程的适定性研究
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023033
Chengfeng Sun, Shan Jiang, Hui Liu
{"title":"Study on the well-posedness of stochastic Boussinesq equations with Navier boundary conditions","authors":"Chengfeng Sun, Shan Jiang, Hui Liu","doi":"10.3934/mfc.2023033","DOIUrl":"https://doi.org/10.3934/mfc.2023033","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220863","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}
引用次数: 0
Generalized interval AOR method for solving interval linear equations 求解区间线性方程的广义区间AOR方法
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023035
Jahnabi Chakravarty, M. Saha
{"title":"Generalized interval AOR method for solving interval linear equations","authors":"Jahnabi Chakravarty, M. Saha","doi":"10.3934/mfc.2023035","DOIUrl":"https://doi.org/10.3934/mfc.2023035","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221069","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}
引用次数: 0
Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators Cheney-Sharma Chlodovsky算子的Durrmeyer变式逼近
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022034
Chandra Prakash, D. K. Verma, N. Deo
{"title":"Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators","authors":"Chandra Prakash, D. K. Verma, N. Deo","doi":"10.3934/mfc.2022034","DOIUrl":"https://doi.org/10.3934/mfc.2022034","url":null,"abstract":"In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified and estimated the convergence properties using of modulus of continuity, Lipschitz- type space, and Ditzian-Totik modulus of continuity. After that, the weighted approximation result is also given. Finally, some results related to the A-statistical convergence of the operators are obtained.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"148 1","pages":"535-545"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73438969","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}
引用次数: 0
Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators 用Kantorovich离散型抽样算子研究Orlicz和Bögel连续函数空间中的收敛定理
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022056
Serkan Ayan, N. Ispir
{"title":"Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators","authors":"Serkan Ayan, N. Ispir","doi":"10.3934/mfc.2022056","DOIUrl":"https://doi.org/10.3934/mfc.2022056","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"25 1","pages":"354-368"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78885437","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}
引用次数: 1
Adaptive attitude determination of bionic polarization integrated navigation system based on reinforcement learning strategy 基于强化学习策略的仿生极化组合导航系统自适应姿态确定
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022014
HuiYi Bao, Tao Du, Luyue Sun
{"title":"Adaptive attitude determination of bionic polarization integrated navigation system based on reinforcement learning strategy","authors":"HuiYi Bao, Tao Du, Luyue Sun","doi":"10.3934/mfc.2022014","DOIUrl":"https://doi.org/10.3934/mfc.2022014","url":null,"abstract":"The bionic polarization integrated navigation system includes three-axis gyroscopes, three-axis accelerometers, three-axis magnetometers, and polarization sensors, which provide pitch, roll, and yaw. When the magnetometers are interfered or the polarization sensors are obscured, the accuracy of attitude will be decreased due to abnormal measurement. To improve the accuracy of attitude of the integrated navigation system under these complex environments, an adaptive complementary filter based on DQN (Deep Q-learning Network) is proposed. The complementary filter is first designed to fuse the measurements from the gyroscopes, accelerometers, magnetometers, and polarization sensors. Then, a reward function of the bionic polarization integrated navigation system is defined as the function of the absolute value of the attitude angle error. The action-value function is introduced by a fully-connected network obtained by historical sensor data training. The strategy can be calculated by the deep Q-learning network and the action that optimal action-value function is obtained. Based on the optimized action, three types of integration are switched automatically to adapt to the different environments. Three cases of simulations are conducted to validate the effectiveness of the proposed algorithm. The results show that the adaptive attitude determination of bionic polarization integrated navigation system based on DQN can improve the accuracy of the attitude estimation.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"96 1","pages":"161-177"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82211802","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}
引用次数: 2
Revisiting Mazur separable quotient problem (1932) 再论Mazur可分离商问题(1932)
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022063
M. López-Pellicer, S. López-Alfonso, S. Moll-López
{"title":"Revisiting Mazur separable quotient problem (1932)","authors":"M. López-Pellicer, S. López-Alfonso, S. Moll-López","doi":"10.3934/mfc.2022063","DOIUrl":"https://doi.org/10.3934/mfc.2022063","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"156 1","pages":"453-459"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77479829","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}
引用次数: 0
Output feedback control of interval type-2 T-S fuzzy fractional order systems subject to actuator saturation 区间2型T-S模糊分数阶系统致动器饱和下的输出反馈控制
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023025
Taoqi Deng, Xuefeng Zhang, Zhe Wang
{"title":"Output feedback control of interval type-2 T-S fuzzy fractional order systems subject to actuator saturation","authors":"Taoqi Deng, Xuefeng Zhang, Zhe Wang","doi":"10.3934/mfc.2023025","DOIUrl":"https://doi.org/10.3934/mfc.2023025","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220953","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}
引用次数: 0
Starlike functions associated with $ tanh z $ and Bernardi integral operator 星形函数关联$ tanh z $和Bernardi积分算子
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022032
Pratima Rai, A. Çetinkaya, Sushil Kumar
{"title":"Starlike functions associated with $ tanh z $ and Bernardi integral operator","authors":"Pratima Rai, A. Çetinkaya, Sushil Kumar","doi":"10.3934/mfc.2022032","DOIUrl":"https://doi.org/10.3934/mfc.2022032","url":null,"abstract":"<p style='text-indent:20px;'>We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function <inline-formula><tex-math id=\"M8\">begin{document}$ tanh z $end{document}</tex-math></inline-formula>. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"29 1","pages":"573-585"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73022462","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}
引用次数: 1
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