Similar Journals
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Nonlinear Analysis : Modelling and Control
Number of Followers: 1  Open Access journalISSN (Print) 1392-5113 - ISSN (Online) 2335-8963 Published by Vilnius University  [38 journals]
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- Fractional elliptic obstacle systems with multivalued terms and nonlocal
operators
Authors: Jinxia Cen Shengda Zeng Anouar Bahrouni
Abstract: In this paper, we introduce and study a fractional elliptic obstacle system, which is composed of two elliptic inclusions with fractional (pi, qi)-Laplace operators, nonlocal functions, and multivalued terms. The weak solution of fractional elliptic obstacle system is formulated by a fully nonlinear coupled system driven by two nonlinear and nonmonotone variational inequalities with constraints. The nonemptiness and compactness of solution set in the weak sense are proved via employing a surjectivity theorem to the multivalued operators formulated by the sum of a multivalued pseudomonotone operator and a maximal monotone operator.
PubDate: Wed, 31 Jul 2024 00:00:00 +000
- Diverse exact solutions to Davey–Stewartson model using modified
extended mapping method
Authors: Karim K. Ahmed Ham Ahmed Niveen M. Badra Mohammad Mirzazadeh Wafaa B. Rabie Mostafa Eslami
Abstract: In this study, we obtain solitary wave solutions and other exact wave solutions for Davey–Stewartson equation (DSE), which explains how waves move through water with a finite depth while being affected by gravity and surface tension. The study is conducted with the aid of the modified extended mapping method (MEMM). A variety of distinct traveling wave solutions are furnished. The obtained solutions comprise dark, bright, and singular solitary wave solutions. Additionally, Jacobi elliptic function solutions, exponential wave solutions, singular periodic wave solutions, rational wave solutions, and periodic wave solutions are also offered. To help readers physically grasp the acquired solutions, graphical representations of some of the extracted solutions are provided.
PubDate: Tue, 30 Jul 2024 00:00:00 +000
- Adaptive synchronization of quaternion-valued neural networks with
reaction–diffusion and fractional order
Authors: Weiwei Zhang Hongyong Zhao Chunlin Sha
Abstract: This paper is dedicated to the study of adaptive finite-time synchronization (FTS) for generalized delayed fractional-order reaction–diffusion quaternion-valued neural networks (GDFORDQVNN). Utilizing the suitable Lyapunov functional, Green’s formula, and inequalities skills, testable algebraic criteria for ensuring the FTS of GDFORDQVNN are established on the basis of two adaptive controllers. Moreover, the numerical examples validate that the obtained results are feasible. Furthermore, they are also verified in image encryption as the application.
PubDate: Fri, 26 Jul 2024 00:00:00 +000
- Fixed point theorems for xi-alpha-eta-Gamma F-fuzzy contraction with an
application to neutral fractional integro-differential equation with
nonlocal conditions
Authors: Abdelhamid Moussaoui Fouad Abdou Ibrahim Amir Stojan Radenović Said Melliani Mhamed Elomari
Abstract: In this study, we define a new fuzzy contraction principle, namely, the concept of ξ-α-η-Γ F-mappings, and prove the existence and uniqueness of the fixed point for such class of mappings. To further demonstrate the validity of our results, we furnish an application to neutral fractional integro-differential equations with nonlocal conditions. The presented results unify, generalize, and enhance a number of prior findings in the literature.
PubDate: Fri, 26 Jul 2024 00:00:00 +000
- Global threshold analysis of an age-space structured disease model with
relapse
Authors: Guoyang Lyu Yutong Guo Jinliang Wang
Abstract: In this paper, an age-space structured disease model with age-dependent relapse rate is investigated. We first prove the well-posedness of the model including the existence and uniqueness of the solution, positivity, and boundedness. By performing the Laplace transformation to renewal equation, we derive the next generation operator, whose spectral radius is defined as the basic reproduction number. By checking the distribution of the roots of the characteristic equation, exploring the strong persistence property of the solution and designing the Lyapunov functionals, we establish the local and global dynamics of the model.
PubDate: Fri, 26 Jul 2024 00:00:00 +000
- Properties of Shannon and Rényi entropies of the Poisson distribution as
the functions of intensity parameter
Authors: Volodymyr Braiman Anatoliy Malyarenko Yuliya Mishura Yevheniia Anastasiia Rudyk
Abstract: We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simple, for Rényi entropy, which depends on additional parameter α > 0, we can characterize it as nontrivial. The proof is based on application of Karamata’s inequality to the terms of Poisson distribution.
PubDate: Mon, 01 Jul 2024 00:00:00 +000
- Optimal control and bifurcation analysis of a delayed fractional-order
SIRS model with general incidence rate and delayed control
Authors: Conghui Xu Yongguang Yu Guojian Ren Xinhui Si
Abstract: A fractional-order generalized SIRS model considering incubation period is established in this paper for the transmission of emerging pathogens. The corresponding Hopf bifurcation is discussed by selecting time delay as the bifurcation parameter. In order to control the occurrence of Hopf bifurcation and achieve better dynamic behaviors, a delayed feedback control is adopted to the model. Further, the delayed fractional-order optimal control problem (DFOCP) is proposed and discussed. The parameters of the proposed model are identified through the measurement data of coronavirus disease 2019 (COVID-19). Based on the results of parameter identification, the corresponding DFOCP with delayed control is numerically solved.
PubDate: Mon, 01 Jul 2024 00:00:00 +000
- Existence of sunny nonexpansive retractions and approximation of fixed
points of a representation of nonexpansive mappings
Authors: Ebrahim Soori Ravi P. Agarwal Donal O'Regan
Abstract: This paper presents an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth uniformly convex Banach space with respect to a left-regular sequence of means defined on a subset of l∞(S). The main results are to establish an existence theorem of a sunny nonexpansive retraction and to create an algorithm for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces.
PubDate: Mon, 01 Jul 2024 00:00:00 +000
- Analyzing crop production: Unraveling the impact of pests and pesticides
through a fractional model
Authors: Navnit Jha Akash Yadav Ritesh Pandey A.K. Misra
Abstract: The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research.
PubDate: Mon, 01 Jul 2024 00:00:00 +000
- Reckoning applications of Z-iteration: Data dependence and solution to a
delay Caputo fractional differential equation
Authors: Salman Zaheer Ankush Chanda Hemant Kumar Nashine
Abstract: In this study, we focus on demonstrating the stability of the three-step Z-iterative scheme within the context of weak contraction mappings as defined by Berinde. Further, we attain results concerning stability, data dependence, and error accumulation of the Z-iterative scheme. This article also includes a comparison of the convergence rates among various established iterative strategies. Several illustrative numerical examples are furnished to validate the accuracy and reliability of our findings. In the same spirit, we present an application that utilises the Z-iterative technique on Banach spaces to attain the solution of a delay Caputo fractional differential equation, building upon our primary findings.
PubDate: Mon, 01 Jul 2024 00:00:00 +000
- Exponential synchronization of dynamical complex networks via random
impulsive scheme
Authors: Bowen Zhou Xiao-Bao Shu Fei Xu Fengyu Yang Ya Wang
Abstract: This paper investigates the synchronization of a complex network based on a class of random impulsive differential equation systems. Based on the random impulsive strategy of Poisson distribution, a random impulsive dynamical network model is constructed. Using the Lyapunov principle, random process theory, linear matrix inequality method, and some basic analysis methods, we realize the global mean-square index synchronization of the model. We then get sufficient criteria for the synchronization. By presenting a numerical example, we verified the validity of the theoretical results.
PubDate: Tue, 25 Jun 2024 00:00:00 +000
- A few generalizations of Kendall’s tau. Part I: Construction
Authors: Martynas Manstavičius
Abstract: Complimenting our earlier work on generalizations of popular concordance measures in the sense of Scarsini for a pair of continuous random variables (X, Y) (such measures can be understood as functions of the bivariate copula C associated with (X, Y)), we focus on generalizations of Kendall’s τ. In Part I, we give two forms of such measures and also provide general bounds for their values, which are sharp in certain cases and depend on the values of Spearman’s ρ and the original Kendall’s τ. Part II is devoted to the intrinsic meaning of presented Kendall’s τ generalizations, their degree as polynomial-type concordance measures, and computational aspects.
PubDate: Tue, 25 Jun 2024 00:00:00 +000
- Singular p-biharmonic problem with the Hardy potential
Authors: Amor Drissi Abdeljabbar Ghanmi Dušan D. Repovš
Abstract: The aim of this paper is to study existence results for a singular problem involving the p-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is established. By using the Nehari manifold method, the multiplicity of solutions is proved. An example is also given to illustrate the importance of these results.
PubDate: Tue, 25 Jun 2024 00:00:00 +000
- Hysteresis and bistability in synaptic transmission modeled as a chain of
biochemical reactions with a positive feedback
Authors: Pranas Katauskis Feliksas Ivanauskas Aidas Alaburda
Abstract: In this paper, we employ computational analysis to investigate the long-term potentiation (LTP) and memory formation in synapses between neurons. We use a mathematical model describing the synaptic transmission as a signal transduction pathway with a positive feedback loop formed by diffusion of nitric oxide (NO) to the presynaptic site. We found that the model of synaptic transmission exhibits a hysteresis-like behavior, where the strength of synaptic transmission depends not just on instantaneous interstimulus intervals, but also on the history of activity. The switching between resting and memory states can be induced by physiologically relevant and moderate (less than 50%) changes in the duration of interstimulus intervals.
PubDate: Tue, 25 Jun 2024 00:00:00 +000
- Large deviations for stochastic predator–prey model with Lévy
noise
Authors: C.S. Sridevi Murugan Suvinthra Krishnan Balachandran
Abstract: This paper discusses the large deviations for stochastic predator–prey model driven by multiplicative Lévy noise. Using Galerkin approximation, we initially prove the existence and uniqueness of solution. Due to the equivalence between Laplace principle and large deviation principle under a Polish space, the method of weak convergence has been followed in order to establish our results for this coupled system of equations.
PubDate: Tue, 25 Jun 2024 00:00:00 +000
- Positive solutions for a Hadamard-type fractional p-Laplacian integral
boundary value problem
Authors: Yihui Xu Feng Wang Donal O'Regan Jiafa Xu
Abstract: In this paper we study the existence of positive solutions to a Hadamard-type fractional integral boundary value problem using fixed point index. We construct a new linear operator and obtain our main results under some conditions concerning the spectral radius of this linear operator. Our method improves and generalizes some results in the literature.
PubDate: Tue, 30 Apr 2024 00:00:00 +000
- Optimal control of an infected prey–predator model with fear effect
Authors: Hong Qiu Tianzi Zhang Rumei Hou
Abstract: In this paper, we propose and analyze a prey–predator model with the functional response of Beddington–DeAngelis and the fear effect that have infection only in prey populations. We determine existence criteria of several equilibria, and the stability at different equilibria are presented. We exert pesticide control over prey and additional food control over predators, the optimal control is obtained by the Pontryagin maximum principle. We confirm that adding controls to the predator and prey yields better results. Further we enrich our analysis with the inclusion of the existence and uniqueness of the optimal control. Finally, some numerical results to illustrate our analysis are presented.
PubDate: Thu, 25 Apr 2024 00:00:00 +000
- Containing an epidemic in the case of running out of treatment: A switched
system approach
Authors: Shraddha Salwahan Syed Abbas Abdessamad Tridane
Abstract: In this paper, we discuss an epidemic switched system. A susceptible–infected–treated model is considered. The course of an epidemic is profoundly influenced by the allocation of resources. If these resources are limited, then we need to devise an optimal distribution strategy. One significant case to study is when the drug supply is insufficient. We study a control problem that minimizes the total outbreak size of the epidemic and optimizes the rate of vaccination/isolation control by minimizing the suitable functional subject to resource constraints. In the end, simulations are performed for illustrations.
PubDate: Wed, 24 Apr 2024 00:00:00 +000
- Soliton-like solutions supported by refined hydrodynamic-type model of an
elastic medium with soft inclusions
Authors: Vsevolod Vladimirov Sergii Skurativskyi
Abstract: A nonlinear elastic medium containing sharp inhomogeneities is considered. The properties of a modified model of such a medium are investigated. The modification consists in including in the asymptotic equation of state those terms that were discarded in the previously considered models. The main purpose of the ongoing research is to analyze the existence, stability, and dynamic properties of soliton-like solutions within the modified model, as well as to compare these solutions with analogous solutions obtained in the previously considered models.
PubDate: Wed, 24 Apr 2024 00:00:00 +000
- The nonlinear contraction in probabilistic cone b-metric spaces with
application to integral equation
Authors: Youssef Achtoun Stojan Radenović Ismail Tahiri Mohammed Lamarti Sefian
Abstract: The probabilistic cone b-metric space is a novel concept that we describe in this study along with some of its fundamental topological properties and instances. We also established the fixed point theorem for the probabilistic nonlinear Banach contraction mapping on this kind of spaces. Many prior findings in the literature are generalized and unified by our findings. In order to illustrate the basic theorem in ordinary cone b-metric spaces, some related findings are also provided with an application to integral equation.
PubDate: Wed, 24 Apr 2024 00:00:00 +000
- A study of nonlinear fractional-order biochemical reaction model and
numerical simulations
Authors: Bheeman Radhakrishnan Paramasivam Chandru Juan J. Nieto
Abstract: This article depicts an approximate solution of systems of nonlinear fractional biochemical reactions for the Michaelis–Menten enzyme kinetic model arising from the enzymatic reaction process. This present work is concerned with fundamental enzyme kinetics, utilised to assess the efficacy of powerful mathematical approaches such as the homotopy perturbation method (HPM), homotopy analysis method (HAM), and homotopy analysis transform method (HATM) to get the approximate solutions of the biochemical reaction model with time-fractional derivatives. The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. The comparison results reveal the complexity of the enzyme process and obtain approximate solutions to the nonlinear fractional differential biochemical reaction model.
PubDate: Wed, 17 Apr 2024 00:00:00 +000
- Delay-induced nutrient recycling in plankton system: Application to
Sundarban mangrove wetland
Authors: Ravikant Singh Archana Ojha Nilesh Kumar Thakur Ranjit Kumar Upadhyay
Abstract: The paper discusses the nutrient–plankton system with effect of time delay in nutrient recycling and toxin determined function response (TDFR). The designed model system explores the delay-induced system dynamics. We present the local stability analysis of interior equilibrium points in absence as well as in presence of time delay. Further, the direction of Hopf bifurcation is obtained. We perform the numerical computation and observe that time delay in nutrient recycling can generate the periodic solution in a stable nutrient–plankton system. Some other essential parameters, such as input concentration of nutrients and natural removal rate of nutrients, also regulate the dynamical system. The system shows Hopf and double-Hopf bifurcation in the presence of time delay. Our study shows that the delay in the nutrient recycling causes instability transition phenomenon. The delay-induced nutrient recycling and different input concentrations of nutrients can regulate the estuarine system. Finally, the stability switching is observed for delayed system.
PubDate: Wed, 17 Apr 2024 00:00:00 +000
- A simulation function approach for optimization by approximate solutions
with an application to fractional differential equation
Authors: Parvaneh Lo'lo' Maryam Shams Stojan Radenović
Abstract: In this work, we study the existence and uniqueness of a common best proximity point for a pair of nonself functions that are not necessarily continuous using the simulation function. In the following, we state important common best proximity point theorems as results of the main theorems of this article. This achievement allows us to have an example that covers our main theorem but does not apply to the Banach contraction principle. Finally, an application of a nonlinear fractional differential equation to support the obtained conclusions.
PubDate: Fri, 05 Apr 2024 00:00:00 +000
- Abstract random differential equations with state-dependent delay using
measures of noncompactness
Authors: Amel Heris Zohra Bouteffal Abdelkrim Salim Mouffak Benchohra Erdal Karapınar
Abstract: This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented.
PubDate: Fri, 05 Apr 2024 00:00:00 +000
- Fractal perspective on dynamics of dark matter and dark energy
interactions
Authors: T.M.C. Priyanka A. Gowrisankar Santo Banerjee
Abstract: In this paper, the dynamics of intricate chaotic attractors of the nonlinear system modeling the dark matter and dark energy interactions is studied indulging fractal–fractional operator in the Caputo sense. The constructed strange attractors witness that the dynamics of the universe components is dominated by the fractal properties. The fractional entropies stemmed from the classical entropy are estimated with fractal parameter and graphically portrayed to measure the randomness of the dynamic variables associated with the proposed dynamical system.
PubDate: Sat, 23 Mar 2024 00:00:00 +000
- Synchronization of delayed stochastic reaction–diffusion Hopfield neural
networks via sliding mode control
Authors: Xiao Liang Yiyi Yang Ruili Wang Jiangtao Chen
Abstract: Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.
PubDate: Sat, 23 Mar 2024 00:00:00 +000
- Existence of solutions for a fractional Riemann–Stieltjes integral
boundary value problem
Authors: Yanfang Li Donal O’Regan Jiafa Xu
Abstract: In this paper, we study a Riemann–Liouville-type fractional Riemann–Stieltjes integral boundary value problem under some conditions regarding the spectral radius of the relevant linear operator. The existence of nontrivial solutions is obtained using topological degree, and our results improve and generalize some results in the literature.
PubDate: Sat, 23 Mar 2024 00:00:00 +000
- Controllability of psi-Hilfer fractional differential equations with
infinite delay via measure of noncompactness
Authors: Inzamamul Haque Javid Ali Juan J. Nieto
Abstract: In this article, we study the controllability of ψ-Hilfer fractional differential equations with infinite delay. Sufficient conditions for controllability results are obtained by using the notion of the measure of noncompactness and the Mönch fixed point theorem. The novel feature of this study is to inquire into the controllability notion by using ψ-Hilfer fractional derivative, the generalized variant of the Hilfer derivative. Finally, we provide a numerical example to illustrate our main result.
PubDate: Fri, 01 Mar 2024 00:00:00 +000
- Dynamics analysis of a nonlinear controlled predator–prey model with
complex Poincaré map
Authors: Huidong Cheng Xin Zhang Tonghua Zhang Jingli Fu
Abstract: In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.
PubDate: Fri, 01 Mar 2024 00:00:00 +000
- Comparative analysis of classical and stochastic Maccari system of
nonlinear equations
Authors: Muhammad Sajid Iqbal Mustafa Inc Saba Sohail Adil Raheem Shabbir Hussain Emad E. Mahmoud
Abstract: In this paper, the exact solutions of classical and stochastic Maccari system is constructed. The exact comparative solutions are examined and plotted. Interesting results in the case of multiplicative noise are formulated and graphically elaborated. The applications of the stochastic Maccari system are added for the physical purpose. The existence of results for the real part of underlying system are discussed first time for a priori estimates. The perturbations, which disturbed the formation of Langmuir waves, are geometrically expressed in this article. Due to the presence of multiplicative noise term, our system brings a real flavor to the dynamics of the problem.
PubDate: Fri, 23 Feb 2024 00:00:00 +000
