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A note on product-convolution for generalized subexponential distributions 关于广义次指数分布乘积卷积的一个注记
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-09-20 DOI: 10.15388/namc.2022.27.29405
D. Konstantinides, R. Leipus, J. Šiaulys
{"title":"A note on product-convolution for generalized subexponential distributions","authors":"D. Konstantinides, R. Leipus, J. Šiaulys","doi":"10.15388/namc.2022.27.29405","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29405","url":null,"abstract":"In this paper, we consider the stability property of the class of generalized subexponential distributions with respect to product-convolution. Assuming that the primary distribution is in the class of generalized subexponential distributions, we find conditions for the second distribution in order that their product-convolution belongs to the class of generalized subexponential distributions as well. The similar problem for the class of generalized subexponential positively decreasing-tailed distributions is considered.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48657606","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}
引用次数: 4
Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks 整数阶和分数阶延迟BAM神经网络分岔行为的比较研究
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-07-25 DOI: 10.15388/namc.2022.27.28491
Changjin Xu, D. Mu, Zixin Liu, Yicheng Pang, Maoxin Liao, Peiluan Li, Lingyun Yao, Qiwen Qin
{"title":"Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks","authors":"Changjin Xu, D. Mu, Zixin Liu, Yicheng Pang, Maoxin Liao, Peiluan Li, Lingyun Yao, Qiwen Qin","doi":"10.15388/namc.2022.27.28491","DOIUrl":"https://doi.org/10.15388/namc.2022.27.28491","url":null,"abstract":"In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42980696","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}
引用次数: 44
On fractional-order symmetric oscillator with offset-boosting control 带有偏置升压控制的分数阶对称振荡器
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-07-19 DOI: 10.15388/namc.2022.27.28279
Changjin Xu, Mati ur Rahman, D. Baleanu
{"title":"On fractional-order symmetric oscillator with offset-boosting control","authors":"Changjin Xu, Mati ur Rahman, D. Baleanu","doi":"10.15388/namc.2022.27.28279","DOIUrl":"https://doi.org/10.15388/namc.2022.27.28279","url":null,"abstract":"This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and uniqueness of solutions for the suggested model are analyzed using the tools from fixed point theory. The symmetric oscillator is analyzed numerically and graphically with various fractional orders. It is observed that the fractional operator has a significant impact on the evolution of the oscillator dynamics showing that the system has a limit-cycle attractor. Offset-boosting control phenomena in the system are also studied with different orders and parameters.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"1 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66951541","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}
引用次数: 24
Superlinear damped vibration problems on time scales with nonlocal boundary conditions 具有非局部边界条件的时间尺度上的超线性阻尼振动问题
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-07-19 DOI: 10.15388/namc.2022.27.28343
Yongfang Wei, Zhanbing Bai
{"title":"Superlinear damped vibration problems on time scales with nonlocal boundary conditions","authors":"Yongfang Wei, Zhanbing Bai","doi":"10.15388/namc.2022.27.28343","DOIUrl":"https://doi.org/10.15388/namc.2022.27.28343","url":null,"abstract":"This paper studies a class of superlinear damped vibration equations with nonlocal boundary conditions on time scales by using the calculus of variations. We consider the Cerami condition, while the nonlinear term does not satisfy Ambrosetti–Rabinowitz condition such that the critical point theory could be applied. Then we establish the variational structure in an appropriate Sobolev’s space, obtain the existence of infinitely many large energy solutions. Finally, two examples are given to prove our results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49380768","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}
引用次数: 0
Well-posedness and stability for fuzzy fractional differential equations 模糊分数阶微分方程的适定性与稳定性
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-07-06 DOI: 10.15388/namc.2022.27.28096
Xuping Zhang, Yanli Xi, D. O’Regan
{"title":"Well-posedness and stability for fuzzy fractional differential equations","authors":"Xuping Zhang, Yanli Xi, D. O’Regan","doi":"10.15388/namc.2022.27.28096","DOIUrl":"https://doi.org/10.15388/namc.2022.27.28096","url":null,"abstract":"In this article, we consider the existence and uniqueness of solutions for a class of initial value problems of fuzzy Caputo–Katugampola fractional differential equations and the stability of the corresponding fuzzy fractional differential equations. The discussions are based on the hyperbolic function, the Banach fixed point theorem and an inequality property. Two examples are given to illustrate the feasibility of our theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47802924","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}
引用次数: 0
On a new variant of F-contractive mappings with application to fractional differential equations 关于F-压缩映射的一个新变种及其在分数阶微分方程中的应用
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-06-30 DOI: 10.15388/namc.2022.27.27963
Pradip Ramesh Patlea, M. Gabeleh
{"title":"On a new variant of F-contractive mappings with application to fractional differential equations","authors":"Pradip Ramesh Patlea, M. Gabeleh","doi":"10.15388/namc.2022.27.27963","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27963","url":null,"abstract":"The present article intends to prove the existence of best proximity points (pairs) using the notion of measure of noncompactness. We introduce generalized classes of cyclic (noncyclic) F-contractive operators, and then derive best proximity point (pair) results in Banach (strictly convex Banach) spaces. This work includes some of the recent results as corollaries. We apply these conclusions to prove the existence of optimum solutions for a system of Hilfer fractionaldifferential equations.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46034637","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}
引用次数: 1
Solvability of a system of integral equations in two variables in the weighted Sobolev space $W^{1,1}_omega(a,b)$ using a generalized measure of noncompactness 加权Sobolev空间$W中双变量积分方程组的可解性^{1,1}_ω（a，b）$使用非紧性的广义测度
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-06-30 DOI: 10.15388/namc.2022.27.27961
Taqi A. M. Shatnawi, A. Boudaoui, W. Shatanawi, Noura Laksaci
{"title":"Solvability of a system of integral equations in two variables in the weighted Sobolev space $W^{1,1}_omega(a,b)$ using a generalized measure of noncompactness","authors":"Taqi A. M. Shatnawi, A. Boudaoui, W. Shatanawi, Noura Laksaci","doi":"10.15388/namc.2022.27.27961","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27961","url":null,"abstract":"In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b). The results were achieved by equipping the space E with the vector-valued norms and using the measure of noncompactness constructed in [F.P. Najafabad, J.J. Nieto, H.A. Kayvanloo, Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations, J. Fixed Point Theory Appl., 22(3), 75, 2020] to applicate the generalized Darbo’s fixed point theorem [J.R. Graef, J. Henderson, and A. Ouahab, Topological Methods for Differential Equations and Inclusions, CRC Press, Boca Raton, FL, 2018].","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49403571","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}
引用次数: 1
Oscillation thresholds via the novel MBR method with application to oncolytic virotherapy 基于新型MBR方法的振荡阈值及其在溶瘤病毒治疗中的应用
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-06-30 DOI: 10.15388/namc.2022.27.27962
B. Buonomo, Rossella Della Marca, S. Rionero
{"title":"Oscillation thresholds via the novel MBR method with application to oncolytic virotherapy","authors":"B. Buonomo, Rossella Della Marca, S. Rionero","doi":"10.15388/namc.2022.27.27962","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27962","url":null,"abstract":"Oncolytic virotherapy is a therapy for the treatment of malignant tumours. In some undesirable cases, the injection of viral particles can lead to stationary oscillations, thus preventing the full destruction of the tumour mass. We investigate the oscillation thresholds in a model for the dynamics of a tumour under treatment with an oncolytic virus. To this aim, we employ the minimum bifurcation roots (MBR) method, which is a novel approach to determine the existence and location of Hopf bifurcations. The application to oncolytic virotherapy confirms how this approach may be more manageable than classical methods based on the Routh–Hurwitz criterion. In particular, the MBR method allows to explicitly identify a range of values in which the oscillation thresholds fall.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47101293","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}
引用次数: 0
Dynamic analysis of a Leslie–Gower-type predator–prey system with the fear effect and ratio-dependent Holling III functional response 具有恐惧效应和比率依赖HollingIII功能反应的Leslie–Gower型捕食者-被捕食系统的动力学分析
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-06-29 DOI: 10.15388/namc.2022.27.27932
Hongyu Chen, Chunrui Zhang
{"title":"Dynamic analysis of a Leslie–Gower-type predator–prey system with the fear effect and ratio-dependent Holling III functional response","authors":"Hongyu Chen, Chunrui Zhang","doi":"10.15388/namc.2022.27.27932","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27932","url":null,"abstract":"In this paper, we extend a Leslie–Gower-type predator–prey system with ratio-dependent Holling III functional response considering the cost of antipredator defence due to fear. We study the impact of the fear effect on the model, and we find that many interesting dynamical properties of the model can occur when the fear effect is present. Firstly, the relationship between the fear coefficient K and the positive equilibrium point is introduced. Meanwhile, the existence of the Turing instability, the Hopf bifurcation, and the Turing–Hopf bifurcation are analyzed by some key bifurcation parameters. Next, a normal form for the Turing–Hopf bifurcation is calculated. Finally, numerical simulations are carried out to corroborate our theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45516403","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}
引用次数: 7
Controllability of nonlinear higher-order fractional damped stochastic systems involving multiple delays 多时滞非线性高阶分数阶阻尼随机系统的可控性
IF 2 3区 数学
Nonlinear Analysis-Modelling and Control Pub Date : 2022-05-24 DOI: 10.15388/namc.2022.27.27587
G. Arthi, K. Suganya, J. Nieto
{"title":"Controllability of nonlinear higher-order fractional damped stochastic systems involving multiple delays","authors":"G. Arthi, K. Suganya, J. Nieto","doi":"10.15388/namc.2022.27.27587","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27587","url":null,"abstract":"This paper is concerned with the controllability problem for higher-order fractional damped stochastic systems with multiple delays, which involves fractional Caputo derivatives of any different orders. In the process of proof, we have proposed the controllability of considered linear system by establishing a controllability Grammian matrix and employing a control function. Sufficient conditions for the considered nonlinear system concerned to be controllable have been derived by constructing a proper control function and utilizing the Banach fixed point theorem with Burkholder–Davis–Gundy’s inequality. Finally, two examples are provided to emphasize the applicability of the derived results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47241337","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}
引用次数: 3
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