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Multilayered neural network for power series-based approximation of fractional delay differential equations Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-17 Manoj Kumar, Sandeep Kumar, Kranti Kumar, Pranay Goswami
This paper trains a multilayered neural network (MLNN) for solving fractional delay differential equations (FDDEs), including nonlinear and singular types. The proposed methodology involves replacing the unknown functions in the equations with a truncated power series expansion. Subsequently, a collection of algebraic equations is solved utilizing an iterative minimization technique that leverages
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The geometrical and physical interpretation of fractional order derivatives for a general class of functions Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-14 Ruby, Moumita Mandal
The aim of this article is to find a geometric and physical interpretation of fractional order derivatives for a general class of functions defined over a bounded or unbounded domain. We show theoretically and geometrically that the absolute value of the fractional derivative value of a function is inversely proportional to the area of the triangle. Further, we prove geometrically that the fractional
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Approximation on Durrmeyer modification of generalized Szász–Mirakjan operators Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-14 Rishikesh Yadav, Vishnu Narayan Mishra, Ramakanta Meher
This paper deals with the approximations of the functions by generalized Durrmeyer operators of Szász–Mirakjan, which are linear positive operators. Several approximation results are presented well, and we estimate the approximation properties along with the order of approximation and the convergence theorem of the proposed operators. For an explicit explanation of the operators, we determine the properties
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Stochastic analysis of two-strain epidemic model with non-monotone incidence rates: Application to COVID-19 pandemic Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-14 Marya Sadki, Zakaria Yaagoub, Karam Allali
This work is devoted to the mathematical analysis of a COVID-19 two-strain epidemic model. The COVID-19 mathematical model described the infection forces of each strain by a nonmonotonic incidence function. First, we establish the well-posedness of the COVID-19 stochastic model in terms of existence and uniqueness of the global positive solution. After that, we investigate the results of the stochastic
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Multiple high‐energy solutions for an elliptic system with critical Hardy–Sobolev nonlinearity Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-16 Maoji Ri, Yongkun Li
This paper discusses the existence of multiple high‐energy solutions for a ‐Laplacian system involving critical Hardy‐Sobolev nonlinearity in . Considering that the “double” lack of compactness in the system is caused by the unboundedness of and the presence of the critical Hardy–Sobolev exponent, we demonstrate the version to of Struwe's classical global compactness result for double ‐Laplace operator
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Critical mass phenomenon for a parabolic–elliptic multispecies chemotaxis system in a two‐dimensional disk Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-16 Hua Zhong
A parabolic–elliptic Keller–Segel model for multipopulations in a two‐dimensional unit ball will be considered in this paper. For the initial boundary value problem with mutually attractive populations, the global existence of bounded solutions has been proved through the logarithmic Hardy–Littlewood–Sobolev inequality for system when the initial masses satisfy the subcritical condition. Moreover,
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Energy decay rate of the wave–wave transmission system with Kelvin–Voigt damping Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-16 Hua‐Lei Zhang
In this paper, we study the energy decay rate of the wave–wave transmission system with Kelvin–Voigt damping on a rectangular domain. The damping is imposed on one of wave equations. By the separation of variables method and the frequency domain method, we show that the optimal energy decay rate of the system is , which is independent of wave speeds.
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Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-16 Dongping Li, Yankai Li, Xiaozhou Feng, Changtong Li, Yuzhen Wang, Jie Gao
This article examines a new family of (p,q)‐Laplacian type nonlinear fractional impulsive differential coupled equations involving both the ‐Caputo fractional derivative and –Riemann–Liouville fractional integral. With the help of Nehari manifold in critical point theory and fractional calculus properties, we obtain the existence of at least one nontrivial ground state solution for the coupled system
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Variational approach to a symmetric boundary value problem generated by a system of equations and separated boundary conditions Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-15 Ekin Uğurlu
This work provides some information on the eigenvalues and eigenfunctions of a problem which is constructed by a system of equations and symmetric boundary conditions that includes the ordinary second‐order Sturm–Liouville boundary value problem. In particular, we show that the problem has an infinite number of discrete eigenvalues with a greatest lower bound and the corresponding eigenfunctions are
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On a singular mathematical model for brain lactate kinetics Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-13 Nour Ali, Hussein Fakih, Ali Wehbe
In this paper, we consider a singular nonlinear differential system that characterizes the intricate dynamics of brain lactate kinetics between cells and capillaries, as described by System (1.1) below. We begin by establishing the existence and uniqueness of nonnegative solutions for our system through the application of Schauder's fixed-point theorem. Subsequently, we explore the behavior of these
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Optimal control problem with nonlinear fractional system constraint applied to image restoration Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-14 Abdelghafour Atlas, Jamal Attmani, Fahd Karami, Driss Meskine
This study aims to investigate a novel nonlinear optimization problem that incorporate a partial differential equation (PDE) constraint for image denoising in the context of mixed noise removal. Based on ‐norm and decomposition approach, we develop a nonlinear system that involves the fractional Laplacian operator. Based on Schauder's fixed point theorem, we establish the existence and uniqueness of
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Issue Information Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-13
No abstract is available for this article.
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Application of flatlet oblique multiwavelets to solve the fractional stochastic integro‐differential equation using Galerkin method Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-13 Safar Irandoust‐Pakchin, Somaiyeh Abdi‐Mazraeh, Mohamed Adel
This study introduces a new numerical approach named flatlet oblique multiwavelets (FOMW) to solve fractional‐order stochastic integro‐differential equation (FSI‐DE). The FOMW is used to create an operational matrix of the stochastic integral, which helps transform the FSI‐DE into a linear system of algebraic equations. This method requires only a small number of basis functions to achieve satisfactory
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Comparison of optimal harvesting policies with general logistic growth and a general harvesting function Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-13 Miguel Reis, Nuno M. Brites, Carla Santos, Cristina Dias
This paper explores stochastic differential equation models to characterize the growth dynamics of a stock modeled by generalized logistic growth under a general harvesting function. The latter function adds diminishing marginal productivity to effort increases, while the former incorporates several well‐known growth functions as particular instances. In order to obtain optimal policies, a Crank–Nicolson
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Characterization of dual curves using the theory of infinitesimal bending Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-13 Marija S. Najdanović
In this paper, we generalize the main ideas and statements of the theory of infinitesimal bending in Euclidean 3‐space to dual curves in the dual 3‐space . The basic condition we introduce is the invariance of the dual arc length with appropriate precision. Necessary and sufficient conditions for the dual field to be an infinitesimal bending field are given. Some useful formulas and facts about dual
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On blow‐up phenomena for a weakly dissipative periodic two‐component b$$ b $$‐family system revisited Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-13 Xiaofang Dong
In this paper, we mainly revisit a weakly dissipative periodic two‐component ‐family system. Considering the dissipative effect, the local well‐posedness is first obtained for the system by applying the Kato's semigroup theory. We then utilize the characteristics line method to get one blow‐up criterion with the dispersive parameter . Finally, the other blow‐up criterion is derived with regard as considering
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Editorial on special issue “physically relevant moving boundary problems” Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-12 Irina Nizovtseva, Dmitri Alexandrov
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Fractal dimension of random attractors for nonautonomous stochastic strongly damped wave equations on ℝN Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-12 Yanjiao Li, Xiaojun Li
In this article, we investigate the dynamics of a nonautonomous stochastic strongly damped wave equation defined on . We first use the energy equation and tail‐estimates to prove the asymptotic compactness of the solutions and obtain the existence of a unique pullback random attractor for the equation with critical nonlinearity. Then, we give an upper bound of fractal dimension of the random attractor
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Bifurcation analysis of a discrete Leslie–Gower predator–prey model with slow–fast effect on predator Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-12 Ahmad Suleman, Abdul Qadeer Khan, Rizwan Ahmed
Understanding and accounting for the slow–fast effect are crucial for accurately modeling and predicting the dynamics of predator–prey models, emphasizing the importance of considering the relative speeds of interacting populations in ecological research. This paper examines a predator–prey interaction to study its complex dynamics due to its slow–fast effect on predator populations. The occurrence
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Stabilization by discrete‐time feedback control for highly nonlinear hybrid neutral stochastic functional differential equations with infinite delay Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-12 Han Yu, Ailong Wu
The problem of stabilizing an unstable highly nonlinear hybrid neutral stochastic functional differential equation with infinite delay (HNSFDEwID) is addressed in this article. The objective of this study is to propose a discrete‐time feedback control (DTFC) approach for stabilizing the original system. Sufficient conditions are derived for the existence and uniqueness of the system's solution, as
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Rogue waves solutions on the elliptic background of an extended (3 + 1)‐dimensional nonlinear Schrödinger equation Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-11 Wang Tang, Guo‐Fu Yu
We construct rogue wave solutions of an extended (3 + 1)‐dimensional nonlinear Schrödinger equation on the Jacobian elliptic function background. The modulational stability of the plane wave background is analyzed. We derive the periodic wave solutions and non‐periodic wave solutions of the Lax spectral problem. Making use of the non‐periodic solutions, we construct rogue waves on the cnoidal background
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On radially symmetric oscillations of a collisional cold plasma Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-11 Olga S. Rozanova, Maria I. Delova
We study the influence of the friction term on the radially symmetric solutions of the repulsive Euler–Poisson equations with a non‐zero background, corresponding to cold plasma oscillations in multiple spatial dimensions. It is shown that for any arbitrarily small non‐negative constant friction coefficient, there exists a neighborhood of the zero equilibrium in the norm such that the solution of the
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Uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-11 Fuyi Li, Xiaoting Li, Zhanping Liang
In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in . Under suitable conditions, we prove that, for any given positive integer , the problem we considered has at most one solution possessing exactly nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc.
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Effect of unfavorable regions on the spreading solution in a diffusion equation Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-11 Pengchao Lai, Junfan Lu
We consider a diffusion equation on the real line with growth rates (reaction terms) being negative in a bounded unfavorable region and bistable on two sides. The equation can be used to model a species living in a habitat with a polluted or hunting zone but still tries to survive or even spread to the whole space. Using the zero number argument, we first show the general convergence to stationary
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An improved nonlinear anisotropic model with p(x)‐growth conditions applied to image restoration and enhancement Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-11 Hamza Alaa, Nour Eddine Alaa, Anass Bouchriti, Abderrahim Charkaoui
This work proposes a novel nonlinear parabolic equation with ‐growth conditions for image restoration and enhancement. Based on the generalized Lebesgue and Sobolev spaces with variable exponent, we demonstrate the well‐posedness of the proposed model. As a first result, we prove the existence of a weak solution to our model when the reaction term is bounded by a suitable function. Secondly, we use
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On control intervals of chaos with Fréchet derivative of certain iterations as discrete dynamical system in Banach spaces Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-11 Derya Sekman, Vatan Karakaya
Dynamical systems are one of the interesting concepts where iteration algorithms and chaos can be considered together. In iteration algorithms, one of the basic concepts of fixed point theory, it is well known that the behavior of the iteration mechanism is chaotic if the original transformation is taken as chaotic. One of the natural ways to transform a chaotic system into a dynamical system is through
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A q$$ q $$‐Erkuş–Srivastava polynomials operator Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-08 Purshottam Narain Agrawal, Behar Baxhaku, Jitendra Kumar Singh
Chan et al. (Integral Transforms Spec. Funct. 12 (2), 139–148, (2001)) constructed a multivariable extension of the Lagrange polynomials, popularly known as the Chan–Chyan–Srivastava polynomials. Altin and Erkuş (Integral Transforms Spec. Funct. 17, 239–244, (2006)) proposed Lagrange–Hermite polynomials in several variables. Erkuş and Srivastava (Integral Transforms Spec. Funct., 17, 267–273, (2006))
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Improvements in the estimation of the Weibull tail coefficient: A comparative study Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-06 Lígia Henriques-Rodrigues, Frederico Caeiro, M. Ivette Gomes
The Weibull tail-coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull-type tails. Several distributions, such as normal, Gamma, Weibull, and logistic distributions, exhibit this type of tail behavior. The WTC, denoted by θ$$ \theta $$, is a parameter in a right-tail function of the form F‾(x):=1−F(x)=:e−H(x)$$ \overline{F}(x):= 1-F(x)=: {\
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Non-singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)-dimensional nonlinear evolution equation Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-05 Kang-Jia Wang, Feng Shi, Peng Xu, Shuai Li
This research mainly concerned with some new solutions of the (3 + 1)-dimensional nonlinear evolution equation (NEE). First, we extract the resonant multiple soliton solutions (RMSSs) by taking advantage of the linear superposition principle (LSP) and weight algorithm (WA). Then the non-singular complexiton and singular complexiton solutions are developed by introducing pairs of the conjugate parameters
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Passivity-based boundary control for stochastic Korteweg–de Vries–Burgers equations Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-05 Shuang Liang, Kai-Ning Wu
The passivity-based boundary control is considered for stochastic Korteweg–de Vries–Burgers (SKdVB) equations. Both the stochastic input strictly passive (SISP) and stochastic output strictly passive (SOSP) are studied. By introducing Lyapunov functionals and Wirtinger's inequality, sufficient criteria are derived to establish SISP and SOSP for SKdVB equations with boundary disturbances. Moreover,
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Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-05 Akuro Big-Alabo, Peter Brownson Alfred
The Helmholtz oscillator is a nonlinear mixed-parity oscillator that models the asymmetric vibrations of many engineering and scientific systems. This paper investigated a general and completely integrable form of the Helmholtz oscillator and derived its exact periodic solution from the first integral of the governing differential equation. The considered Helmholtz oscillator has general linear and
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Well posedness and stability result of Lord–Shulman system with microtemperature effects: The case ξμ∗=μ02 Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-04 Marwa Boudeliou, Abdelhak Djebabla, Tijani A. Apalara
In this study, we investigate the Lord–Shulman porous elastic system with dissipation caused by the microtemperature effects. Here, the thermal conduction has a single-phase-lag that acts as a relaxation time and the energy associated with the solution is not required to be positive definite (ξμ∗=μ02)$$ \left(\xi {\mu}^{\ast }={\mu}_0^2\right) $$. We introduce a stability number
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Robust passivity analysis for uncertain stochastic switched inertial neural networks with time-varying delay under a new state-dependent switching law Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-04 A. Nasira Banu, K. Banupriya, V. Dhanya
This paper addresses the problems of passivity and robust passivity for a class of stochastic switched inertial neural networks (SSINNs) with time-varying parametric uncertainties. First, the original inertial neural networks can be converted into first-order differential systems using a suitable variable transformation approach. Moreover, by using a proper Lyapunov–Krasovskii functional (LKF) theory
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Dissipative structures for the system of Moore–Gibson–Thompson thermoelasticity in the whole space Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-05 Marta Pellicer, Ramon Quintanilla, Yoshihiro Ueda
We investigate the dissipative structure for the system of Moore–Gibson–Thompson (MGT) thermoelasticity in the whole space. To analyze the dissipative structure, it is very useful to rewrite the equations into a symmetric hyperbolic system and apply the so‐called stability condition. When we rewrite our system into the symmetric hyperbolic form in the multidimensional case, it is important to take
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Exponential stability and relative controllability of first‐order delayed integro‐differential systems with impulses Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-05 Bakhtawar Pervaiz, Akbar Zada, Ioan‐Lucian Popa, Sana Ben Moussa, Afef Kallekh
We establish sufficient conditions for the exponential stability of nonsingular impulsive delayed integro‐differential systems. Our approach to addressing nonsingular differential problems involves the application of permutable matrices and their associated delayed exponential. Furthermore, we investigate the controllability of a nonlinear impulsive and delayed problem by employing the corresponding
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Solving second‐order differential equations in terms of confluent Heun's functions Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-05 Shayea Aldossari
This paper presents an algorithm that checks if a given second‐order homogeneous linear differential equation can be reduced to the confluent Heun's equation by using the change of variables transformation and the exp‐product transformation. The main purpose of this paper is finding solutions in terms of the confluent Heun's functions for the given differential equation.
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Norm retrieval algorithms: A new frame theory approach Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-04 Fahimeh Arabyani‐Neyshaburi, Ali Akbar Arefijamaal, Ramin Farshchian, Rajab Ali Kamyabi‐Gol
In this paper, we introduce a new approach based on the excess components of a frame for recognizing norm retrieval frames (NRFs) in finite‐dimensional Hilbert spaces. This method leads to a complete characterization of NRFs in and and then to 1‐excess NRFs in . This approach is not only more effective in higher dimensions for detecting NRF than the previous approaches but is also applicable to constructing
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Time‐optimal feedback control of nonlocal Hilfer fractional state‐dependent delay inclusion with Clarke's subdifferential Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-04 Vidushi Tripathi, Sanjukta Das
In this article, we discuss the optimal feedback control of nonlocal Hilfer fractional state‐dependent delay inclusion of order with Clarke's subdifferential. Firstly, we establish the existence of mild solutions for this class of equations by employing the Krasnoselskii's fixed‐point theorem, without using Lipschitz conditions. Subsequently, we develop set of sufficient assumptions, utilizing Cesari
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Sign‐changing solutions of fractional Laplacian system with critical exponent Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-04 Qi Li, Shixin Wen
This paper deals with the following fractional Laplacian system with critical exponent: where is a bounded smooth open connected set in is the fractional critical Sobolev exponent, and is the first eigenvalue of fractional Laplacian under the condition in . We prove that, for each fixed and slightly smaller than , the above system with admits a sign‐changing solution in the following sense: one component
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Boundary estimation and cascade control for a Lorenz‐like system Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-02 Yin Li, Aibin Zang
In this paper, we devoted to investigate a hyperelliptic estimate of the ultimate bound and positively invariant set for the new system via the Lyapunov function method. Furthermore, we obtained the global exponential attractive set , which is an exponential decay rate. The rate of the trajectories of the system going from the exterior to the interior of the set . Numerical simulations are presented
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The effect of migration on the transmission of HIV/AIDS using a fractional model: Local and global dynamics and numerical simulations Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-02 A. Alla Hamou, E. Azroul, S. L'Kima
Human immunodeficiency virus (HIV) is a serious disease that threatens and affects capital stock, population composition, and economic growth. This research paper aims to study the mathematical modeling and disease dynamics of HIV/acquired immunodeficiency syndrome (AIDS) with memory effect. We propose two fractional models in the Caputo sense for HIV/AIDS with and without migration. First, we prove
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Event‐triggered H∞$$ {H}_{\infty } $$ performance state estimation for neural networks with time‐varying delay Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-02 Wenlong Xue, Yanfang Gao
The issue of event‐triggered performance state estimation for neural networks with time‐varying delays is addressed in this paper. An innovative event‐triggered approach is presented, designed to strike a harmonious equilibrium between the state estimator's performance and the communication bandwidth of the network. The proposed approach captures the relationship between the time‐varying delay and
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Modeling blood alcohol concentration using fractional differential equations based on the ψ$$ \psi $$‐Caputo derivative Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-01 Om Kalthoum Wanassi, Delfim F. M. Torres
We propose a novel dynamical model for blood alcohol concentration that incorporates ‐Caputo fractional derivatives. Using the generalized Laplace transform technique, we successfully derive an analytic solution for both the alcohol concentration in the stomach and the alcohol concentration in the blood of an individual. These analytical formulas provide us a straightforward numerical scheme, which
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Periodicity, stability, and synchronization of solutions of hybrid coupled dynamic equations with multiple delays Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-01 Divya Agrawal, Soniya Dhama, Marko Kostić, Syed Abbas
This paper explores general coupled dynamic equations on time scales with multiple delays and investigates the existence of periodic solutions using the coincidence degree theory approach. The model studied includes the mathematical models of Nicholson, Mackey–Glass, and Lasota–Wazewska as special cases. Furthermore, we demonstrate that the solutions are not only asymptotically stable but also exponentially
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Another look at addition theorems for vector spherical wavefunctions Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-01 P. A. Martin
Addition theorems for vector spherical wavefunctions are widely used, but they are complicated. A critical survey of methods for their derivation is offered. Then, one derivation is given in detail, combining elementary techniques with known results for scalar addition theorems.
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Dynamical properties, chirped solutions, and chaotic behaviors of the extended nonlinear Schrödinger equation Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-03-01 Jia‐Xuan Tang
In this paper, we focus on an extended nonlinear Schrödinger equation describing the pulse propagation in a nonlinear Schrödinger equation with self‐steepening and magneto‐optic effects. The existence of periodic and solitary solutions are proved based on the bifurcation method, and also, the Hamiltonian properties and the classification of its equilibrium points are obtained. The chirped solutions
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Essential norm of linear operators from general weighted-type spaces to Banach spaces and some applications Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Stevo Stević
We present a result concerning the essential norm of linear operators mapping some general weighted-type spaces of holomorphic functions on the open unit ball in ℂn$$ {\mathrm{\mathbb{C}}}^n $$ to Banach spaces. As some applications, we compare essential norms of a product-type operator of integral type and a weighted composition operator between some of the general weighted-type spaces.
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The τ$$ \tau $$‐symmetries and Lie algebra structure of the Blaszak–Marciniak lattice equation Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-29 Jian‐bing Zhang, Qi Chen
A general approach is developed for discriminating strong and hereditary symmetric operators. The recursion operator of the Blaszak–Marciniak (BM) equation hierarchy is proved to be strong and hereditary symmetric. As an example of discrete soliton equations related to matrix spectral problems, the ‐symmetries and Lie algebra structure of the BM equation are built firstly.
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Scattering by a biisotropic obstacle and the properties of the Beltrami spherical vector waves Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-29 Gerhard Kristensson
In this paper, we take a fresh look at the determination of the transition matrix for a homogeneous, biisotropic particle employing the Null‐field approach. The condition for passivity of the material is discussed. In particular, we focus on some previously unproved properties of the Beltrami spherical vector waves, such as completeness, orthogonality, and linear independence, which are all instrumental
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Boundedness criteria for the commutators of fractional integral and fractional maximal operators on Morrey spaces generated by the Gegenbauer differential operator Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Elman J. Ibrahimov, Saadat A. Jafarova
In this paper, we find the necessary and sufficient conditions for the boundedness of commutators of fractional integral and fractional maximal operators generated by Gegenbauer differential operator in ‐Morrey spaces. We consider the generalized shift operator, associated with the Gegenbauer differential operator . The commutator of fractional integral and the commutator of fractional maximal operator
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Robust sliding mode control for robot manipulators with analysis on trade‐off between reaching time and L∞$$ {\mathcal{L}}_{\infty } $$ gain Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Oe Ryung Kang, Jung Hoon Kim
This paper provides a new sliding mode control (SMC) approach, by which both the nominal and robust stability associated with a trajectory tracking problem for an uncertain robot manipulator are achieved. More precisely, the new control law consists of linear and nonlinear functions of tracking errors, in which the former is for the nominal stability and the latter is to ensure the robust stability
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Finite‐time stability of reaction–diffusion genetic regulatory networks with nondifferential time‐varying mixed delays Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Xinran She, Leimin Wang
This paper explores the finite‐time stability of reaction–diffusion genetic regulatory networks with time‐varying mixed delays. These delays encompass discrete delays and distributed delays. Unlike many existing studies, this paper assumes that both types of delays are bounded and continuous, without requiring differentiability. Additionally, the analysis combines the inequality approach and comparison
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Classification of quasi‐product production models with minimal isoquants Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Crina Daniela Neacşu, Nasser Bin Turki, Gabriel‐Eduard Vîlcu
The study of the minimality of (hyper)surfaces is a fundamental problem in mathematics with major applications in both fundamental and applied sciences. Recently, the minimality of production models in microeconomics has been investigated by several authors who obtained important classification results for quasi‐sum and quasi‐product production functions with two and three inputs. In the present work
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Residually continuous pullback attractors for stochastic discrete plate equations Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Kaili Han, Yangrong Li, Huan Xia
For a nonautonomous stochastic discrete plate equation driven by multiplicative noise, we prove the unique existence of a pullback random attractor, which is a family of pullback‐attracting random compact sets parameterized by time and samples. We then establish the residual dense continuity of the pullback random attractor on the time‐sample plane with respect to the Hausdorff metric. Even without
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Non‐auto Darboux transformation for N$$ N $$‐soliton solutions of the non‐isospectral Korteweg–de Vries hierarchy Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Xing‐yu Liu, Bin‐he Lu, Da‐jun Zhang
The usual non‐isospectral Korteweg–de Vries (KdV) hierarchy (see Equation 4) does not have auto Darboux transformations. In this paper, we present a non‐auto Darboux transformation for this hierarchy, from which we are able to construct its ‐soliton solutions. An explicit formula of the solutions with zero background is given, and solutions are illustrated.
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Matrix projective synchronization and mechanical analysis of unified chaotic system Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-28 Vijay K. Shukla, Mahesh C. Joshi, Grienggrai Rajchakit, Juan E. Nápoles Valdes, Prashant K. Mishra
This article explores the mechanical analysis of a unified chaotic system and matrix projective synchronization (MPS). The sufficient conditions to achieve MPS of unified chaotic system have derived. The mechanics of unified chaotic system have been examined in contrast with Kolmogorov system, Euler equation, and Hamiltonian function. The Casimir energy function is also introduced to analyze the system
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Approximate-analytical iterative approach to time-fractional Bloch equation with Mittag–Leffler type kernel Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-22 Akshey, Twinkle R. Singh
The paper aims to analyze the fractional Bloch equation with Caputo and Atangana–Baleanu–Caputo (ABC) derivative having a nonsingular kernel. The fixed point theorem is used to prove the existence and uniqueness of the proposed equation. Furthermore, the approximate-analytical solution of the proposed equation is obtained by Aboodh transform iterative method (ATIM) in the form of a convergent series
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Unraveling forward and backward source problems for a nonlocal integrodifferential equation: A journey through operational calculus for Dzherbashian‐Nersesian operator Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-24 Anwar Ahmad, Muhammad Ali, Salman A. Malik
This article primarily aims at introducing a novel operational calculus of Mikusiński's type for the Dzherbashian‐Nersesian operator. Using this calculus, we are able to derive exact solutions for the forward and backward source problems of a differential equation that features Dzherbashian‐Nersesian operator in time and intertwined with nonlocal boundary conditions. The initial condition is expressed
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Uncertainty principles for windowed coupled fractional Fourier transform Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-24 Mawardi Bahri, Fitriyani Syamsuddin, Nasrullah Bachtiar, Amir Kamal Amir
The windowed coupled fractional Fourier transform was recently proposed in the literature. It may be considered as a generalized version of the windowed fractional Fourier transform. In this study, we first present various basic properties of the windowed coupled fractional Fourier transform including linearity, shifting, modulation, parity, orthogonality relation, and inversion formula. Further, the
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Global regularity for the 2D micropolar Rayleigh–Bénard convection system with velocity zero dissipation and temperature critical diffusion Math. Methods Appl. Sci. (IF 2.9) Pub Date : 2024-02-24 Baoquan Yuan, Changhao Li
This paper studies the global regularity problem for the 2D micropolar Rayleigh–Bénard convection system with velocity zero dissipation, micro‐rotation velocity Laplace dissipation, and temperature critical diffusion. By introducing a combined quantity and using the technique of Littlewood–Paley decomposition, we establish the global regularity result of solutions to this system.