Pub Date : 2023-10-27DOI: 10.15388/namc.2023.28.33474
Muthukrishnan Latha Maheswari, Kolathur Srinivasan Keerthana Shri, Elsayed M. Elsayed
This study examines the existence and uniqueness of the solution to the coupled system of the ψ-Hilfer nonlinear implicit fractional multipoint boundary value problem. The uniqueness is shown by the Banach contraction principle, and the existence is shown by Krasnosel’skii’s fixed point theorem in a special working space. An example is presented to verify our results. The existence and uniqueness of the solution are analysed graphically.
{"title":"Multipoint boundary value problem for a coupled system of psi-Hilfer nonlinear implicit fractional differential equation","authors":"Muthukrishnan Latha Maheswari, Kolathur Srinivasan Keerthana Shri, Elsayed M. Elsayed","doi":"10.15388/namc.2023.28.33474","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33474","url":null,"abstract":"This study examines the existence and uniqueness of the solution to the coupled system of the ψ-Hilfer nonlinear implicit fractional multipoint boundary value problem. The uniqueness is shown by the Banach contraction principle, and the existence is shown by Krasnosel’skii’s fixed point theorem in a special working space. An example is presented to verify our results. The existence and uniqueness of the solution are analysed graphically.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"9 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.15388/namc.2023.28.33471
Javad Alidousti, Mojtaba Fardi, Shrideh Al-Omari
In this paper, a fractional density-dependent prey–predator model has been considered. Certain reading of local and global stabilities of an equilibrium point of a system was extracted and conducted by applying fractional systems’ stability theorems along with Lyapunov functions. Meanwhile, the persistence of the aforementioned system has been discussed and claimed to imply a local asymptotic stability for the given positive equilibrium point. Moreover, the presented model was extended to a periodic impulsive model for the prey population. Such an expansion was implemented through the periodic catching of the prey species and the periodic releasing of the predator population. By studying the effect of changing some of the system’s parameters and drawing their bifurcation diagram, it was observed that different periodic solutions appear in the system. However, the effect of an impulse on the system subjects the system to various dynamic changes and makes it experience behaviors including cycles, period-doubling bifurcation, chaos and coexistence as well. Finally, by comparing the fractional system with the classic one, it has been concluded that the fractional system is more stable than its classical one.
{"title":"Bifurcation analysis of impulsive fractional-order Beddington–DeAngelis prey–predator model","authors":"Javad Alidousti, Mojtaba Fardi, Shrideh Al-Omari","doi":"10.15388/namc.2023.28.33471","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33471","url":null,"abstract":"In this paper, a fractional density-dependent prey–predator model has been considered. Certain reading of local and global stabilities of an equilibrium point of a system was extracted and conducted by applying fractional systems’ stability theorems along with Lyapunov functions. Meanwhile, the persistence of the aforementioned system has been discussed and claimed to imply a local asymptotic stability for the given positive equilibrium point. Moreover, the presented model was extended to a periodic impulsive model for the prey population. Such an expansion was implemented through the periodic catching of the prey species and the periodic releasing of the predator population. By studying the effect of changing some of the system’s parameters and drawing their bifurcation diagram, it was observed that different periodic solutions appear in the system. However, the effect of an impulse on the system subjects the system to various dynamic changes and makes it experience behaviors including cycles, period-doubling bifurcation, chaos and coexistence as well. Finally, by comparing the fractional system with the classic one, it has been concluded that the fractional system is more stable than its classical one.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"7 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-25DOI: 10.15388/namc.2023.28.33429
Marimuthu Mohan Raja, Velusamy Vijayakumar, Juan J. Nieto, Sumati Kumari Panda, Anurag Shukla, Kottakkaran Sooppy Nisar
In this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed point theorem. Initially, we introduce the idea of mild solution for fractional hemivariational inequalities. Next, the approximate controllability results of semilinear control problems were then established. Moreover, we will move on to the system involving nonlocal conditions. Finally, an example is provided in support of the main results we acquired.
{"title":"An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators","authors":"Marimuthu Mohan Raja, Velusamy Vijayakumar, Juan J. Nieto, Sumati Kumari Panda, Anurag Shukla, Kottakkaran Sooppy Nisar","doi":"10.15388/namc.2023.28.33429","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33429","url":null,"abstract":"In this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed point theorem. Initially, we introduce the idea of mild solution for fractional hemivariational inequalities. Next, the approximate controllability results of semilinear control problems were then established. Moreover, we will move on to the system involving nonlocal conditions. Finally, an example is provided in support of the main results we acquired.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"51 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135167496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the exponential convergence of delayed inertial Cohen–Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results.
{"title":"Global exponential convergence of delayed inertial Cohen–Grossberg neural networks","authors":"Yanqiu Wu, Nina Dai, Zhengwen Tu, Liangwei Wang, Qian Tang","doi":"10.15388/namc.2023.28.33431","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33431","url":null,"abstract":"In this paper, the exponential convergence of delayed inertial Cohen–Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"420 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135168336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-28DOI: 10.15388/namc.2023.28.33088
J. Llibre, C. Valls
The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. Here for the first time, we classify all the local phase portraits of its equilibrium points, and we provide the global phase portraits on the 2-dimensional sphere of the boundary of the ball B.
{"title":"Phase portraits on the unit sphere of the stretch-twist-fold flow","authors":"J. Llibre, C. Valls","doi":"10.15388/namc.2023.28.33088","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33088","url":null,"abstract":"The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. Here for the first time, we classify all the local phase portraits of its equilibrium points, and we provide the global phase portraits on the 2-dimensional sphere of the boundary of the ball B.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41568718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-20DOI: 10.15388/namc.2023.28.33003
Xia Zhou, Chunya Huang, Ping Li, Zhongjun Ma, Jinde Cao
The issue of leader-following identical consensus for nonlinear Markov jump multiagent systems (NMJMASs) under deception attacks (DAs) or denial-of-service (DoS) attacks is investigated in this paper. The Bernoulli random variable is introduced to describe whether the controller is injected with false data, that is, whether the systems are subjected to DAs. A connectivity recovery mechanism is constructed to maintain the connection among multi-agents when the systems are subjected to DoS attack. The impulsive control strategy is adopted to ensure that the systems can normally work under DAs or DoS attacks. Based on graph theory, Lyapunov stability theory, and impulsive theory, using the Lyapunov direct method and stochastic analysis method, the sufficient conditions of identical consensus for Markov jump multi-agent systems (MJMASs) under DAs or DoS are obtained, respectively. Finally, the correctness of the results and the effectiveness of the method are verified by two numerical examples.
{"title":"Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse","authors":"Xia Zhou, Chunya Huang, Ping Li, Zhongjun Ma, Jinde Cao","doi":"10.15388/namc.2023.28.33003","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33003","url":null,"abstract":"The issue of leader-following identical consensus for nonlinear Markov jump multiagent systems (NMJMASs) under deception attacks (DAs) or denial-of-service (DoS) attacks is investigated in this paper. The Bernoulli random variable is introduced to describe whether the controller is injected with false data, that is, whether the systems are subjected to DAs. A connectivity recovery mechanism is constructed to maintain the connection among multi-agents when the systems are subjected to DoS attack. The impulsive control strategy is adopted to ensure that the systems can normally work under DAs or DoS attacks. Based on graph theory, Lyapunov stability theory, and impulsive theory, using the Lyapunov direct method and stochastic analysis method, the sufficient conditions of identical consensus for Markov jump multi-agent systems (MJMASs) under DAs or DoS are obtained, respectively. Finally, the correctness of the results and the effectiveness of the method are verified by two numerical examples.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48764437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-27DOI: 10.15388/namc.2023.28.32845
Luhong Ye, Hongyong Zhao, Daiyong Wu
In this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display umericalsimulations to verify the theoretical outcomes.
{"title":"Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting","authors":"Luhong Ye, Hongyong Zhao, Daiyong Wu","doi":"10.15388/namc.2023.28.32845","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32845","url":null,"abstract":"In this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display umericalsimulations to verify the theoretical outcomes.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42526617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-19DOI: 10.15388/namc.2023.28.32711
Hami Gündoğdu, M. Öztürk, Ö. F. Gözükizil
This paper introduces new generalizations of the C-condition for (ψ; γ)-mappings in modular metric spaces. We extend the fixed point results for such mappings yielding the generalized C-condition in metric spaces to modular ones.We proved the existence and uniqueness of solutions in modular metric spaces for these kinds of mappings. We give an example to emphasize that our results work in the difference between modularmetric spaces and usual ones. Moreover, we consider some initial and boundary value problems to support the results obtained here. We examine the existence and uniqueness of the solutions for the problems in modular metric spaces.
{"title":"Fixed point theorems of new generalized C-conditions for ( psi; gamma)-mappings in modular metric spaces and its applications","authors":"Hami Gündoğdu, M. Öztürk, Ö. F. Gözükizil","doi":"10.15388/namc.2023.28.32711","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32711","url":null,"abstract":"This paper introduces new generalizations of the C-condition for (ψ; γ)-mappings in modular metric spaces. We extend the fixed point results for such mappings yielding the generalized C-condition in metric spaces to modular ones.We proved the existence and uniqueness of solutions in modular metric spaces for these kinds of mappings. We give an example to emphasize that our results work in the difference between modularmetric spaces and usual ones. Moreover, we consider some initial and boundary value problems to support the results obtained here. We examine the existence and uniqueness of the solutions for the problems in modular metric spaces.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42116477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-14DOI: 10.15388/namc.2023.28.32675
U. Patel, S. Radenović
In the piece of this note, we mention various Suzuki-type fuzzy contractive inequalities in 1-Z-complete fuzzy metric-like spaces for uniqueness and existence of a fixed point and prove a few fuzzy fixed point theorems, which are appropriate generalizations of some of the latest famed results in the literature. Mainly, we generalize fuzzy Θ-contraction in terms of Suzuki-type fuzzy Θ-contraction and also fuzzy ϓ-contractive mapping in view of Suzuki-type. For this new group of Suzuki-type functions, acceptable conditions are formulated to ensure the existence of a unique fixed point. The attractive beauty of this fuzzy distance space lies in the symmetry of its variables, which play a crucial role in the construction of our contractive conditions to ensure the solution. Furthermore, a lot of considerable examples are presented to illustrate the significance of our results. In the end, we have discussed an application in an extensive way for the solution of a nonlinear fractional differential equation via Suzuki-type fuzzy contractive mapping.
{"title":"Suzuki-type fuzzy contractive inequalities in 1-Z-complete fuzzy metric-like spaces with an application","authors":"U. Patel, S. Radenović","doi":"10.15388/namc.2023.28.32675","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32675","url":null,"abstract":"In the piece of this note, we mention various Suzuki-type fuzzy contractive inequalities in 1-Z-complete fuzzy metric-like spaces for uniqueness and existence of a fixed point and prove a few fuzzy fixed point theorems, which are appropriate generalizations of some of the latest famed results in the literature. Mainly, we generalize fuzzy Θ-contraction in terms of Suzuki-type fuzzy Θ-contraction and also fuzzy ϓ-contractive mapping in view of Suzuki-type. For this new group of Suzuki-type functions, acceptable conditions are formulated to ensure the existence of a unique fixed point. The attractive beauty of this fuzzy distance space lies in the symmetry of its variables, which play a crucial role in the construction of our contractive conditions to ensure the solution. Furthermore, a lot of considerable examples are presented to illustrate the significance of our results. In the end, we have discussed an application in an extensive way for the solution of a nonlinear fractional differential equation via Suzuki-type fuzzy contractive mapping.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42378810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.15388/namc.2023.28.32643
Qiang Li, Lishan Liu, Xuan Wu
This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field.
{"title":"Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay","authors":"Qiang Li, Lishan Liu, Xuan Wu","doi":"10.15388/namc.2023.28.32643","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32643","url":null,"abstract":"This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47005980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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