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 begin{document}$ E_{0} $end{document}, endemic equilibrium point begin{document}$ E_{*} $end{document}, and basic reproduction number begin{document}$ R_0 $end{document} have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.
In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point begin{document}$ E_{0} $end{document}, endemic equilibrium point begin{document}$ E_{*} $end{document}, and basic reproduction number begin{document}$ R_0 $end{document} have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.
{"title":"Stability analysis of fractional order modelling of social media addiction","authors":"Pradeep Malik, Deepika","doi":"10.3934/mfc.2022040","DOIUrl":"https://doi.org/10.3934/mfc.2022040","url":null,"abstract":"<p style='text-indent:20px;'>In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point <inline-formula><tex-math id=\"M1\">begin{document}$ 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}
{"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}
{"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}
{"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}
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.
{"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}
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 begin{document}$ tanh z $end{document}. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.
We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function begin{document}$ tanh z $end{document}. 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.
{"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}
{"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}
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}
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.
{"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}
In the present article, we study a generalization of Szász operators by Gould-Hopper polynomials. First, we obtain an estimate of error of the rate of convergence by these operators in terms of first order and second order moduli of continuity. Then, we derive a Voronovkaya-type theorem for these operators. Lastly, we derive Grüss-Voronovskaya type approximation theorem and Grüss-Voronovskaya type asymptotic result in quantitative form.
{"title":"On Szász-Durrmeyer type modification using Gould Hopper polynomials","authors":"Karunesh Singh, P. Agrawal","doi":"10.3934/mfc.2022011","DOIUrl":"https://doi.org/10.3934/mfc.2022011","url":null,"abstract":"In the present article, we study a generalization of Szász operators by Gould-Hopper polynomials. First, we obtain an estimate of error of the rate of convergence by these operators in terms of first order and second order moduli of continuity. Then, we derive a Voronovkaya-type theorem for these operators. Lastly, we derive Grüss-Voronovskaya type approximation theorem and Grüss-Voronovskaya type asymptotic result in quantitative form.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"87 1","pages":"123-135"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84420470","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：