https://www.journals.vu.lt/nonlinear-analysis/gateway/plugin/WebFeedGatewayPlugin/atomNonlinear Analysis: Modelling and Control2023-09-01T09:47:45+00:00Prof. Romas Baronasnonlinear@mii.vu.ltOpen Journal Systems<p>Founded in 1997 and dedicated to publishing interdisciplinary works on nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. Indexed in the <em>Scopus</em> (Q2) database since 2009 and in the<em> Web of Science</em> (Q1) database since 2010.</p>https://www.journals.vu.lt/nonlinear-analysis/article/view/33088Phase portraits on the unit sphere of the stretch-twist-fold flow2023-09-01T09:47:45+00:00Jaume LlibreClaudia Valls
<p>The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball <span style="text-decoration: overline;"><em>B</em></span> 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 <span style="text-decoration: overline;"><em>B</em></span>.</p>
2023-08-28T00:00:00+00:00Copyright (c) 2023 Jaume Llibre | Claudia Vallshttps://www.journals.vu.lt/nonlinear-analysis/article/view/33003Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse2023-09-01T09:47:31+00:00Xia ZhouChunya HuangPing LiZhongjun MaJinde Cao
<p>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.</p>
2023-08-20T00:00:00+00:00Copyright (c) 2023 Xia Zhou | Chunya Huang | Ping Li | Zhongjun Ma | Jinde Caohttps://www.journals.vu.lt/nonlinear-analysis/article/view/32845Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting2023-09-01T09:47:15+00:00Luhong YeHongyong ZhaoDaiyong Wu
<p>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 umerical simulations to verify the theoretical outcomes.</p>
2023-07-27T00:00:00+00:00Copyright (c) 2023 Luhong Ye | Hongyong Zhao | Daiyong Wuhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32711Fixed point theorems of new generalized C-conditions for (psi; gamma)-mappings in modular metric spaces and its applications2023-09-01T09:46:58+00:00Hami GündoğduMahpeyker ÖztürkÖmer Faruk Gözükızıl
<p>This paper introduces new generalizations of the <em>C</em>-condition for (<em>ψ</em>; <em>γ</em>)-mappings in modular metric spaces. We extend the fixed point results for such mappings yielding the generalized <em>C</em>-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.</p>
2023-07-19T00:00:00+00:00Copyright (c) 2023 Hami Gündoğdu | Mahpeyker Öztürk | Ömer Faruk Gözükızılhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32675Suzuki-type fuzzy contractive inequalities in 1-Z-complete fuzzy metric-like spaces with an application2023-09-01T09:46:32+00:00Uma Devi PatelStojan Radenović
<p>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 <em>Θ</em>-contraction in terms of Suzuki-type fuzzy <em>Θ</em>-contraction and also fuzzy <em>ϓ</em>-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.</p>
2023-07-14T00:00:00+00:00Copyright (c) 2023 Uma Devi Patel | Stojan Radenovićhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32643Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay2023-09-01T09:46:17+00:00Qiang LiLishan LiuXu Wu
<p>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.</p>
2023-07-10T00:00:00+00:00Copyright (c) 2023 Qiang Li | Lishan Liu | Xu Wuhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32600Optimal control analysis of a malaria transmission model with applications to Democratic Republic of Congo2023-09-01T09:46:03+00:00Jinhui LiMojeeb AL-Rahman EL-Nor OsmanZhidong Teng
<p>In this paper, a dynamical model of malaria transmission with vector-bias and timedependent controls is investigated. The controls include the RTS,S malaria vaccine, using insecticide-treated mosquito net, treatment of infectious human, and indoor spraying. For constant controls, the existence and stability of equilibrium, as well as the existence of backward bifurcation, are obtained. The sensitivity analysis quantifies the impact of parameters and controls on the basic reproduction number. For time-dependent controls, by using the Pontryagin’s maximum principle the existence and expression of optimal controls are established. As an application of the model and control strategies, the malaria transmission and controls in Democratic Republic of Congo are discussed. To be specific, we simulate the reported cases of Democratic Republic of Congo by World Health Organization and predict the trends. Cost-effectiveness analysis and numerical simulations show that combining all controls can minimize the number of infected humans to the full extent, using insecticide-treated mosquito net is the most cost-effectiveness strategy, combining RTS,S malaria vaccine with using insecticide-treated mosquito net and treatment of infectious human is also cost-effective among all the strategies with good effect.</p>
2023-06-30T00:00:00+00:00Copyright (c) 2023 Jinhui Li | Mojeeb AL-Rahman EL-Nor Osman | Zhidong Tenghttps://www.journals.vu.lt/nonlinear-analysis/article/view/32599Dynamic analysis and optimal control of a novel fractional-order 2I2SR rumor spreading model2023-09-01T09:45:45+00:00Maolin YeJiarong LiHaijun Jiang
<p>In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then the next-generation matrix method is used to calculate the threshold. Furthermore, the stability of rumor-free/spreading equilibrium is discussed based on fractional-order Routh–Hurwitz stability criterion, Lyapunov function method, and invariance principle. Next, the necessary conditions for fractional optimal control are obtained. Finally, some numerical simulations are given to verify the results.</p>
2023-06-30T00:00:00+00:00Copyright (c) 2023 Maolin Ye | Jiarong Li | Haijun Jianghttps://www.journals.vu.lt/nonlinear-analysis/article/view/32177Nontrivial solutions for an asymptotically linear Delta alpha-Laplace equation2023-09-01T09:45:13+00:00Jiafa XuJia ChenDonal O'Regan
<p>In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition.</p>
2023-06-30T00:00:00+00:00Copyright (c) 2023 Jiafa Xu | Jia Chen | Donal O'Reganhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32142Weak Wardowski contractive multivalued mappings and solvability of generalized phi-Caputo fractional snap boundary inclusions2023-09-01T09:44:54+00:00Hossein JafariBabak MohammadiVahid ParvanehMohammad Mursaleen
<p>In this paper, we introduce the notion of weak Wardowski contractive multivalued mappings and investigate the solvability of generalized '-Caputo snap boundary fractional differential inclusions. Our results utilize some existing results regarding snap boundary fractional differential inclusions. An example is given to illustrate the applicability of our main results.</p>
2023-06-30T00:00:00+00:00Copyright (c) 2023 Hossein Jafari | Babak Mohammadi | Vahid Parvaneh | Mohammad Mursaleenhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32505Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks2023-06-30T21:29:29+00:00Shenglong ChenHong-Li LiLeimin WangCheng HuHaijun JiangZhiming Li
<p>Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations.</p>
2023-06-19T00:00:00+00:00Copyright (c) 2023 Shenglong Chen | Hong-Li Li | Leimin Wang | Cheng Hu | Haijun Jiang | Zhiming Lihttps://www.journals.vu.lt/nonlinear-analysis/article/view/32395Optimal control for a two-sidedly degenerate aggregation equation2023-06-30T21:29:27+00:00Mostafa BendahmaneFahd KaramiElmahdi ErrajiAbdelghafour AtlasLekbir Afraites
<p>In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming. We establish the wellposedness (existence and uniqueness) for the weak solution of the direct problem by means of an auxiliary nondegenerate aggregation equation, the Faedo–Galerkin method (for the existence result) and duality method (for the uniqueness). Moreover, for the adjoint problem, we prove the existence result of minimizers and first-order necessary conditions. The main novelty of this work concerns the presence of a control to our nonlocal degenerate aggregation model. Our results are complemented with some numerical simulations.</p>
2023-06-04T00:00:00+00:00Copyright (c) 2023 Mostafa Bendahmane | Fahd Karami | Elmahdi Erraji | Abdelghafour Atlas | Lekbir Afraiteshttps://www.journals.vu.lt/nonlinear-analysis/article/view/32277Event-triggered leader-following formation control of general linear multi-agent systems with distributed infinite input time delays2023-06-30T21:29:25+00:00Ya DengWei Zhu
<p>By employing event-triggered control technique, this paper investigates the leaderfollowing formation control problem of general linear multi-agent systems with distributed infinite input time delays. To decrease computing costs, a novel event-triggered formation protocol taking into consideration of the distributed infinite time delays between agents is put forward. Under the designed triggering function and triggering condition, a sufficient condition on leader-following formation is obtained, and then the Zeno-behavior of triggering time sequences is excluded for the concerned closed-loop system. The continuous update of controller for each agent is avoided. Finally, the correctness and the effectiveness of these theoretical results are demonstrated by two numerical examples.</p>
2023-05-23T00:00:00+00:00Copyright (c) 2023 Ya Deng | Wei Zhuhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32230An immunity-structured SEIRS epidemic model with variable infectivity and spatial heterogeneity2023-06-30T21:29:23+00:00Vladas SkakauskasAlgirdas Ambrazevičius
<p>A mathematical model is proposed for the spread of an epidemic disease of agedependent infectivity through an asexual population with spatial heterogeneity, assuming that some individuals recover from the disease with temporary immunity, another part recover with permanent immunity, and the last part recover with no immunity. The demographic changes such as births and deaths due to natural causes and the chronological age of individuals are not taken into account. The model is based on a system of partial integro-differential equations including a differential equation to describe the evolution of individuals who have recovered with temporary immunity. The existence and uniqueness of the globally defined solution is proved, and its long-time behaviour is studied.</p>
2023-05-22T00:00:00+00:00Copyright (c) 2023 Vladas Skakauskas | Algirdas Ambrazevičiushttps://www.journals.vu.lt/nonlinear-analysis/article/view/32197Design-based composite estimation of small proportions in small domains2023-06-30T21:29:22+00:00Andrius Čiginas
<p>Traditional direct estimation methods are inefficient for domains of a survey population with small sample sizes. To estimate the domain proportions, we combine the direct estimators and the regression-synthetic estimators based on domain-level auxiliary information. For the case of small true proportions, we propose the design-based linear combination that is a robust alternative to the empirical best linear unbiased predictor (EBLUP) based on the Fay–Herriot model.</p> <p>We imitate the Lithuanian Labor Force Survey, where we estimate the proportions of the unemployed and employed in municipalities. We show where the proposed design-based composition and estimator of its mean square error are competitive for EBLUP and its accuracy estimation.</p>
2023-05-10T00:00:00+00:00Copyright (c) 2023 Andrius Čiginashttps://www.journals.vu.lt/nonlinear-analysis/article/view/32192Steady-state bifurcation of FHN-type oscillator on a square domain2023-06-30T21:29:20+00:00Chunrui ZhangXiaoxiao LiuBaodong Zheng
<p>The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the <em>D</em><sub>4</sub>-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations. In this paper, taking the FHN model as an example, we give a explicit calculation formula of normal form for the simple and double Turing bifurcation of the reaction-diffusion equation with Dirichlet boundary conditions and defined on a square space, and we also obtain a method for the calculation of the existence of spatially inhomogeneous steady-state solutions. This paper provides a theoretical basis for exploring and predicting the pattern formation of spatial multimode interaction.</p>
2023-05-09T00:00:00+00:00Copyright (c) 2023 Chunrui Zhang | Xiaoxiao Liu | Baodong Zhenghttps://www.journals.vu.lt/nonlinear-analysis/article/view/32130Solvability for a Hadamard-type fractional integral boundary value problem2023-06-30T21:29:19+00:00Jiafa XuJie LiuDonal O'Regan
<p>In this paper, we study an integral boundary value problem involving a Hadamard-type fractional differential equation. Using fixed point theory and upper-lower solutions, we present some sufficient conditions to obtain existence theorems of positive solutions for the problem. Examples are provided to illustrate our results.</p>
2023-04-27T00:00:00+00:00Copyright (c) 2023 Jiafa Xu | Jie Liu | Donal O'Reganhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32127MHD flow of non-Newtonian ferro nanofluid between two vertical porous walls with Cattaneo–Christov heat flux, entropy generation, and time-dependent pressure gradient2023-06-30T21:29:16+00:00Anala Subramanyam ReddySomasundaram RajamaniAli J. ChamkhaSuripeddi SrinivasKrishnamurthy Jagadeshkumar
<p>This article studies the magnetohydrodynamic flow of non-Newtonian ferro nanofluid subject to time-dependent pressure gradient between two vertical permeable walls with Cattaneo–Christov heat flux and entropy generation. In this study, blood is considered as non-Newtonian fluid (couple stress fluid). Nanoparticles’ shape factor, Joule heating, viscous dissipation, and radiative heat impacts are examined. This investigation is crucial in nanodrug delivery, pharmaceutical processes, microelectronics, biomedicines, and dynamics of physiological fluids. The flow governing partial differential equations are transformed into the system of ordinary differential equations by deploying the perturbation process and then handled with Runge–Kutta 4th-order procedure aided by the shooting approach. Hamilton–Crosser model is employed to analyze the thermal conductivity of different shapes of nanoparticles. The obtained results reveal that intensifying Eckert number leads to a higher temperature, while the reverse is true for increased thermal relaxation parameter. Heat transfer rate escalates for increasing thermal radiation. Entropy dwindles for intensifying thermal relaxation parameter.</p>
2023-04-27T00:00:00+00:00Copyright (c) 2023 Anala Subramanyam Reddy | Somasundaram Rajamani | Ali J. Chamkha | Suripeddi Srinivas | Krishnamurthy Jagadeshkumarhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32118An analysis of approximate controllability for Hilfer fractional delay differential equations of Sobolev type without uniqueness2023-06-30T21:29:14+00:00Murugesan JohnsonKrishnan KavithaDimplekumar ChalishajarMuslim MalikVelusamy VijayakumarAnurag Shukla
<p>This study focused on the approximate controllability results for the Hilfer fractional delay evolution equations of the Sobolev type without uniqueness. Initially, the Lipschitz condition is derived from the hypothesis, which is represented by a measure of noncompactness, in particular, nonlinearity. We also examined the continuity of the solution map of the Sobolev type of Hilfer fractional delay evolution equation and the topological structure of the solution set. Furthermore, we prove the approximate controllability of the fractional evolution equation of the Sobolev type with delay. Finally, we provided an example to illustrate the theoretical results.</p>
2023-04-26T00:00:00+00:00Copyright (c) 2023 Murugesan Johnson | Krishnan Kavitha | Dimplekumar Chalishajar | Muslim Malik | Velusamy Vijayakumar | Anurag Shuklahttps://www.journals.vu.lt/nonlinear-analysis/article/view/31878New results of global Mittag-Leffler synchronization on Caputo fuzzy delayed inertial neural networks2023-06-30T21:29:12+00:00Xiangnian YinHongmei ZhangHai ZhangWeiwei ZhangJinde Cao
<p>This article is devoted to discussing the problem of global Mittag-Leffler synchronization (GMLS) for the Caputo-type fractional-order fuzzy delayed inertial neural networks (FOFINNs). First of all, both inertial and fuzzy terms are taken into account in the system. For the sake of reducing the influence caused by the inertia term, the order reduction is achieved by the measure of variable substitution. The introduction of fuzzy terms can evade fuzziness or uncertainty as much as possible. Subsequently, a nonlinear delayed controller is designed to achieve GMLS. Utilizing the inequality techniques, Lyapunov’s direct method for functions and Razumikhin theorem, the criteria for interpreting the GMLS of FOFINNs are established. Particularly, two inferences are presented in two special cases. Additionally, the availability of the acquired results are further confirmed by simulations.</p>
2023-03-30T00:00:00+00:00Copyright (c) 2023 Xiangnian Yin | Hongmei Zhang | Hai Zhang | Weiwei Zhang | Jinde Caohttps://www.journals.vu.lt/nonlinear-analysis/article/view/31721Optimal control results for impulsive fractional delay integrodifferential equations of order 1 < r < 2 via sectorial operator2023-06-08T13:33:59+00:00Murugesan JohnsonMarimuthu Mohan RajaVelusamy VijayakumarAnurag ShuklaKottakkaran Sooppy NisarHadi Jahanshahi
<p>This research investigates the existence of nonlocal impulsive fractional integrodifferential equations of order 1 < <em>r</em> < 2 with infinite delay. To begin with, we discuss the existence of a mild solution for the fractional derivatives by using the sectorial operators, the nonlinear alternative of the Leray–Schauder fixed point theorem, mixed Volterra–Fredholm integrodifferential types, and impulsive systems. Furthermore, we develop the optimal control results for the given system. The application of our findings is demonstrated with the help of an example.</p>
2023-03-09T00:00:00+00:00Copyright (c) 2023 Murugesan Johnson | Marimuthu Mohan Raja | Velusamy Vijayakumar | Anurag Shukla | Kottakkaran Sooppy Nisar | Hadi Jahanshahihttps://www.journals.vu.lt/nonlinear-analysis/article/view/32123Existence of multiple positive solutions for a third-order boundary value problem with nonlocal conditions2023-04-30T21:05:20+00:00Sergey Smirnov
<p>We study the existence of multiple positive solutions for a nonlinear third-order differential equation subject to various nonlocal boundary conditions. The boundary conditions that we study contain Stieltjes integral and include the special cases of m-point conditions and integral conditions. The main tool in the proof of our result is Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider examples.</p>
2023-04-26T00:00:00+00:00Copyright (c) 2023 Sergey Smirnovhttps://www.journals.vu.lt/nonlinear-analysis/article/view/32119Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space2023-04-30T21:05:18+00:00Parvaneh Lo'Lo'Maryam ShamsManuel De la Sen
<p>In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said <em>Z</em>-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation.</p>
2023-04-26T00:00:00+00:00Copyright (c) 2023 Parvaneh Lo'Lo' | Maryam Shams | Manuel De la Senhttps://www.journals.vu.lt/nonlinear-analysis/article/view/31958Global dynamics of a dengue fever model incorporating transmission seasonality2023-04-30T21:05:15+00:00Min ZhuTingting FengYong XuJinde Cao
<p>The changes of seasons cause that the transmission of dengue fever is characterized by periodicity. We develop a dengue fever transmission model incorporating seasonal periodicity and spatial heterogeneity. Based on the well-posedness of solution for this model, we propose its basic reproduction number <em>R</em><sub>0</sub>, and we discuss the properties of this number including its limiting form when the diffusion coefficients change. Moreover, the dynamical behavior of this model infers that if <em>R</em><sub>0</sub> ⩽ 1, then the disease-free periodic solution is globally asymptotically stable, and if <em>R</em><sub>0</sub> > 1, then the model possesses a positive periodic solution, which is globally asymptotically stable. These theoretical findings are further illustrated by the final numerical simulations. Additionally, we add that the similar problem has been investigated by M. Zhu and Y. Xu [A time-periodic dengue fever model in a heterogeneous environment, <em>Math. Comput. Simul.</em>, 155:115–129, 2019] in which some dynamical results have been studied only on the cases <em>R</em><sub>0</sub> < 1 and <em>R</em><sub>0</sub> > 1. Our results not only include the scenario on the case <em>R</em><sub>0</sub> = 1, but also involve the more succinct conditions on the cases <em>R</em><sub>0</sub> < 1 and <em>R</em><sub>0</sub> > 1.</p>
2023-04-12T00:00:00+00:00Copyright (c) 2023 Min Zhu | Tingting Feng | Yong Xu | Jinde Caohttps://www.journals.vu.lt/nonlinear-analysis/article/view/31866Analysis and soliton solutions of biofilm model by new extended direct algebraic method2023-04-30T21:05:13+00:00Muhammad Sajid IqbalMustafa IncSaba SohailHina KhurshidKalsoom Chishti
<p>In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.</p>
2023-03-29T00:00:00+00:00Copyright (c) 2023 Muhammad Sajid Iqbal | Mustafa Inc | Saba Sohail | Hina Khurshid | Kalsoom Chishtihttps://www.journals.vu.lt/nonlinear-analysis/article/view/31801On the solvability of the Atangana–Baleanu fractional evolution equations: An integral contractor approach2023-04-30T21:05:12+00:00Renu ChaudharySimeon Reich
<p>We present existence and controllability results for mild solutions to the Atangana–Baleanu fractional evolution equations. We prove our results by applying bounded integral contractors and a sequencing technique. In contrast to the papers available in the literature, in order to establish our controllability results, we need not define the induced inverse of the controllability operator, and the pertinent nonlinear function need not necessarily satisfy a Lipschitz condition. In addition, we also establish trajectory controllability results. Finally, we discuss an application, which illustrates our results.</p>
2023-04-27T00:00:00+00:00Copyright (c) 2023 Renu Chaudhary | Simeon Reichhttps://www.journals.vu.lt/nonlinear-analysis/article/view/31728Existence of positive solutions for singular p-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term2023-04-30T21:05:10+00:00Limin GuoHaimei LiuCheng LiJingbo ZhaoJiafa Xu
<p>In this paper, based on the properties of Green function and the eigenvalue of a corresponding linear operator, the existence of positive solutions is investigated by spectral analysis for a infinite-points singular p-Laplacian Hadamard fractional differential equation boundary value problem, and an example is given to demonstrate the validity of our main results.</p>
2023-03-11T00:00:00+00:00Copyright (c) 2023 Limin Guo | Haimei Liu | Cheng Li | Jingbo Zhao | Jiafa Xuhttps://www.journals.vu.lt/nonlinear-analysis/article/view/31662Controllability of multi-agent systems with input and communication delays2023-04-30T21:05:06+00:00Yuanchao SiDeyuan MengJinRong Wang
<p>Distributed cooperative control of multi-agent systems is broadly applied in artificial intelligence in which time delay is of great concern because of its ubiquitous. This paper considers the controllability of leader-follower multi-agent systems with input and communication delays. For the first-order systems with input delay, neighbor-based protocol is adopted to realize the interactions among agents, yielding a system with delay existed in state and control input. New notions of interval controllability and interval structural controllability for the system are defined. Algebraic criterion is established for interval controllability, and graph-theoretic interpretation is put forward for the interval structural controllability. Results imply that input delay of the multi-agent systems has significant influence on the interval controllability and interval structural controllability. Corresponding conclusions are generalized to the first-order systems and the high-order ones with communication delays, respectively. Example is attached to illustrate the work.</p>
2023-03-01T00:00:00+00:00Copyright (c) 2023 Yuanchao Si | Deyuan Meng | JinRong Wanghttps://www.journals.vu.lt/nonlinear-analysis/article/view/31609Cattaneo–Christov heat flux impacts on MHD radiative natural convection of Al2O3-Cu-H2O hybrid nanofluid in wavy porous containers using LTNE2023-04-30T21:05:04+00:00Sameh E. AhmedA. MahdyMohamed A. Mansour
<p>This paper aims to examine impacts of Cattaneo–Christov heat flux on the magnetohydrodynamic convective transport within irregular containers in the presence of the thermal radiation. Both of the magnetic field and flow domain are slant with the inclination angles <em>Ω</em> and <em>γ</em>, respectively. The worked fluid is consisting of water (H<sub>2</sub>O) and Al<sub>2</sub>O<sub>3</sub>-Cu hybrid nanoparticles. The enclosures are filled with a porous medium, and the local thermal nonequilibrium (LTNE) model between the hybrid nanofluids and the porous elements are considered. Influences of various types of the obstacles are examined, namely, horizontal cold elliptic, vertical elliptic and cross section ellipsis. The solution methodology is depending on the finite volume method with nonorthogonal grids. The major outcomes revealed that the location (0.75, 0.5) is better for the rate of the flow and temperature gradients. The higher values of <em>H*</em> causes that the solid phase temperature has a similar behavior of the fluid phase temperature indicating to the thermal equilibrium state. Also, the fluid-phase average Nusselt number is maximizing by increasing Cattaneo–Christov heat flux factor.</p>
2023-02-23T00:00:00+00:00Copyright (c) 2023 Sameh E. Ahmed | A. Mahdy | Mohamed A. Mansourhttps://www.journals.vu.lt/nonlinear-analysis/article/view/31563Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network2023-04-30T21:05:02+00:00Xuening XuZhiyong YuDa HuangHaijun Jiang
<p>This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, a distributed optimization algorithm is proposed based on the internal model principle in which the internal model term can effectively compensate for external environmental disturbances. Secondly, the relationship between the optimal solution and the equilibrium point of the system is discussed through the properties of the Laplacian matrix and graph theory. Some sufficient conditions are derived by using the Lyapunov–Razumikhin theory, which ensures all agents asymptotically reach the optimal value of the distributed optimization problem. Moreover, an aperiodic sampled-data control protocol is proposed, which can be well transformed into the proposed time-varying delay protocol and analyzed by using the Lyapunov–Razumikhin theory. Finally, an example is given to verify the effectiveness of the results.</p>
2023-02-22T00:00:00+00:00Copyright (c) 2023 Xuening Xu | Zhiyong Yu | Da Huang | Haijun Jiang