D. Chalishajar, K. Ramkumar, A. Anguraj, K. Ravikumar, M. Diop
This paper is concerned with the controllability results of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, the theory of resolvent operator in the sense of Grimmer and Krasnoselskii fixed point theorem. An example is provided to illustrate the obtained theory.
{"title":"Controllability of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay via resolvent operator","authors":"D. Chalishajar, K. Ramkumar, A. Anguraj, K. Ravikumar, M. Diop","doi":"10.22436/jnsa.015.03.01","DOIUrl":"https://doi.org/10.22436/jnsa.015.03.01","url":null,"abstract":"This paper is concerned with the controllability results of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, the theory of resolvent operator in the sense of Grimmer and Krasnoselskii fixed point theorem. An example is provided to illustrate the obtained theory.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89746096","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, a Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic model with application to COVID-19 is established by capturing the key features of the disease. The global dynamics of the model is analyzed by constructing appropriate Lyapunov functions utilizing the basic reproduction number R0 as an index. We obtain that when R0 < 1, the disease-free equilibrium is globally asymptotically stable. While for R0 > 1, the endemic equilibrium is globally asymptotically stable. Furthermore, we consider the pulse vaccination for the disease and give an impulsive differential equations model. The definition of the basic reproduction number R0 of this system is given by utilizing the next generation operator. By the comparison theorem and persistent theory, we obtain that when R0 < 1, the disease-free periodic solution is globally asymptotically stable. Otherwise, the disease will persist and there will be at least one nontrivial periodic solution. Numerical simulations to verify our conclusions are given at the end of each of these theorems.
{"title":"Threshold dynamics of an SEAIR epidemic model with application to COVID-19","authors":"Zijun Zheng, Youping Yang","doi":"10.22436/jnsa.015.02.05","DOIUrl":"https://doi.org/10.22436/jnsa.015.02.05","url":null,"abstract":"In this paper, a Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic model with application to COVID-19 is established by capturing the key features of the disease. The global dynamics of the model is analyzed by constructing appropriate Lyapunov functions utilizing the basic reproduction number R0 as an index. We obtain that when R0 < 1, the disease-free equilibrium is globally asymptotically stable. While for R0 > 1, the endemic equilibrium is globally asymptotically stable. Furthermore, we consider the pulse vaccination for the disease and give an impulsive differential equations model. The definition of the basic reproduction number R0 of this system is given by utilizing the next generation operator. By the comparison theorem and persistent theory, we obtain that when R0 < 1, the disease-free periodic solution is globally asymptotically stable. Otherwise, the disease will persist and there will be at least one nontrivial periodic solution. Numerical simulations to verify our conclusions are given at the end of each of these theorems.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82923703","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 introduce an inertial hybrid S-iteration algorithm for two asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space. Strong convergence of the iterative scheme is established. Our results improve and extend many recent results in the literature.
{"title":"Inertial hybrid S-iteration algorithm for fixed point of asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space","authors":"M. Harbau, A. Ahmad","doi":"10.22436/jnsa.015.02.04","DOIUrl":"https://doi.org/10.22436/jnsa.015.02.04","url":null,"abstract":"In this paper, we introduce an inertial hybrid S-iteration algorithm for two asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space. Strong convergence of the iterative scheme is established. Our results improve and extend many recent results in the literature.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83197289","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 aim of this paper is to prove Laplace transform of some special functions in term of generalized Meijer G-functions. Some properties of generalized Meijer G-functions will be discussed. We investigate the Laplace transform of different hypergeometric functions in the form of generalized Meijer G-functions and hypergeometric functions. We derive Laplace transform of Bessel k-functions, hyper-Bessel k-functions, incomplete gamma k-function, sine k-integral, sine hyperbolic k-integral, Kelvin k-function in the form of generalized Meijer G-functions. In fact, we provide new approach to find Laplace transform of said functions.
{"title":"Laplace transform of some special functions in terms of generalized Meijer G-functions","authors":"S. Shah, S. Mubeen","doi":"10.22436/jnsa.015.02.03","DOIUrl":"https://doi.org/10.22436/jnsa.015.02.03","url":null,"abstract":"The aim of this paper is to prove Laplace transform of some special functions in term of generalized Meijer G-functions. Some properties of generalized Meijer G-functions will be discussed. We investigate the Laplace transform of different hypergeometric functions in the form of generalized Meijer G-functions and hypergeometric functions. We derive Laplace transform of Bessel k-functions, hyper-Bessel k-functions, incomplete gamma k-function, sine k-integral, sine hyperbolic k-integral, Kelvin k-function in the form of generalized Meijer G-functions. In fact, we provide new approach to find Laplace transform of said functions.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89578489","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 study an initial value problem with fractional Laplacian and a singular integral drift term. This equation quantifies fractal interfaces in statistical mechanics. The singularity of the drift term is a generalization of existing results. Making use of some important boundedness properties of Calderón-Zygmund operator in Lp and Lipschitz spaces, we obtain local and global existence theorems.
{"title":"Local and global existence of a nonlocal equation with a singular integral drift term","authors":"Ying-Ling Lu","doi":"10.22436/jnsa.015.01.05","DOIUrl":"https://doi.org/10.22436/jnsa.015.01.05","url":null,"abstract":"We study an initial value problem with fractional Laplacian and a singular integral drift term. This equation quantifies fractal interfaces in statistical mechanics. The singularity of the drift term is a generalization of existing results. Making use of some important boundedness properties of Calderón-Zygmund operator in Lp and Lipschitz spaces, we obtain local and global existence theorems.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82031560","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}
With the increasing importance of the Mittag-Leffler function in physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper, efforts are made to define the bicomplex extension of the Mittag-Leffler function, and also its analyticity and region of convergence are discussed. Various properties of the bicomplex Mittag-Leffler function including integral representation, recurrence relations, duplication formula, and differential relations are established.
{"title":"Bicomplex Mittag-Leffler function and associated properties","authors":"R. Agarwal, Urvashi Sharma, R. Agarwal","doi":"10.22436/jnsa.015.01.04","DOIUrl":"https://doi.org/10.22436/jnsa.015.01.04","url":null,"abstract":"With the increasing importance of the Mittag-Leffler function in physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper, efforts are made to define the bicomplex extension of the Mittag-Leffler function, and also its analyticity and region of convergence are discussed. Various properties of the bicomplex Mittag-Leffler function including integral representation, recurrence relations, duplication formula, and differential relations are established.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79068483","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 consider a deterministic model explaining how Zika virus is transmitted between human and mosquito. The human population is divided into three groups as susceptible (x1), infected (x2), and treated (x3). Similarly, the mosquito population is divided into susceptible (y1) and infected (y2) groups. First, we conduct the local and global stability of the disease-free and endemic equilibrium points in relation to the basic reproductive number. We also study the sensitivity of the basic reproductive number and the endemic equilibrium point with respect to each parameters used in the model. Furthermore, we apply optimal control theory to show that there are cost effective control methods with the prevention effort (u1) of the contact between human and vector and the effort of treatment (u2) for human. Finally, we provide numerical simulations to support and illustrate some of the theoretical results.
{"title":"Analysis and optimal control of a deterministic Zika virus model","authors":"Dawit Denu, Hyun-Soo Son","doi":"10.22436/jnsa.015.02.02","DOIUrl":"https://doi.org/10.22436/jnsa.015.02.02","url":null,"abstract":"In this paper, we consider a deterministic model explaining how Zika virus is transmitted between human and mosquito. The human population is divided into three groups as susceptible (x1), infected (x2), and treated (x3). Similarly, the mosquito population is divided into susceptible (y1) and infected (y2) groups. First, we conduct the local and global stability of the disease-free and endemic equilibrium points in relation to the basic reproductive number. We also study the sensitivity of the basic reproductive number and the endemic equilibrium point with respect to each parameters used in the model. Furthermore, we apply optimal control theory to show that there are cost effective control methods with the prevention effort (u1) of the contact between human and vector and the effort of treatment (u2) for human. Finally, we provide numerical simulations to support and illustrate some of the theoretical results.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81655044","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 present article aims to study and extend the concepts of Kuratowski ideal convergence of sequence of closed sets in the framework of intuitionistic fuzzy metric spaces and obtain several properties for Kuratowski ideal convergent of sequence of closed sets.
{"title":"Some concepts related to generalized Kuratowski convergence via ideal","authors":"V. Khan, A. Esi, M. Ahmad","doi":"10.22436/jnsa.015.02.01","DOIUrl":"https://doi.org/10.22436/jnsa.015.02.01","url":null,"abstract":"The present article aims to study and extend the concepts of Kuratowski ideal convergence of sequence of closed sets in the framework of intuitionistic fuzzy metric spaces and obtain several properties for Kuratowski ideal convergent of sequence of closed sets.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"98 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76044759","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}
Y. Joresse, Y. Gozo, B. G. Jean-Marc, T. K. Augustin
In this paper we consider a long flexible Euler-Bernoulli beam with boundary conditions imposed at the two ends, the resulting model being called hybrid system. The beam is hybrid in the sense that it holds both rigid and elastic motions. Our main result is to show the existence and uniqueness of the weak solution of close-loop system. The closed-loop system stability is shown through Lyapunov-based analysis.
{"title":"Existence and uniqueness of a hybrid system with variable coefficients","authors":"Y. Joresse, Y. Gozo, B. G. Jean-Marc, T. K. Augustin","doi":"10.22436/jnsa.015.01.06","DOIUrl":"https://doi.org/10.22436/jnsa.015.01.06","url":null,"abstract":"In this paper we consider a long flexible Euler-Bernoulli beam with boundary conditions imposed at the two ends, the resulting model being called hybrid system. The beam is hybrid in the sense that it holds both rigid and elastic motions. Our main result is to show the existence and uniqueness of the weak solution of close-loop system. The closed-loop system stability is shown through Lyapunov-based analysis.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72929852","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, an SIQR-Epidemic transmission model of the non-Markovian infection process and quarantine process in a heterogeneous complex network is established, in which the infection rate and quarantine rate are related to infection age. Next, we use the method of characteristics to transform the model into an integro-differential equation and derive the epidemic threshold of the model. Finally, we focus on the impact of three different infection or quarantine time distributions on the disease transmission and show that infection or quarantine time distribution has a significant effect on the disease dynamics.
{"title":"SIQR dynamics in a random network with heterogeneous connections with infection age","authors":"Hairong Yan, Jinxian Li","doi":"10.22436/jnsa.014.04.02","DOIUrl":"https://doi.org/10.22436/jnsa.014.04.02","url":null,"abstract":"In this paper, an SIQR-Epidemic transmission model of the non-Markovian infection process and quarantine process in a heterogeneous complex network is established, in which the infection rate and quarantine rate are related to infection age. Next, we use the method of characteristics to transform the model into an integro-differential equation and derive the epidemic threshold of the model. Finally, we focus on the impact of three different infection or quarantine time distributions on the disease transmission and show that infection or quarantine time distribution has a significant effect on the disease dynamics.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73844080","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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