This work is concerned with boundary conditions (BCs) for a linearized hyperbolic moment system of the Boltzmann equation in one dimension. We show that even if the usual relaxation stability conditions and the Kreiss condition hold, there exists an exponentially increasing solution to the initial-boundary-value problem (IBVP) of the moment system. To clarify this problem, we check the generalized

This article investigates game-theoretic approaches in a competitive supply chain model with imperfect production and a two-tier credit facility under the environment of carbon emissions. In this environment, we incorporate a manufacturer and two rival retailers who compete against one another for selling price and advertisement of a product, where the members offer trade credit facilities to the downstream

In this paper, the dynamics of stochastic human T-cell leukemia virus type I (HTLV-I) infection model with cytotoxic T lymphocyte (CTL) immune response is investigated. First, we show that the stochastic model exists as a unique positive global solution originating from the positive initial value. Second, we demonstrate that the stochastic model is stochastically permanent and stochastically ultimately

It is eminent that iterative learning control algorithm is of high significance due to its speciality of tracking control for systems developed from real-world phenomena that occurs repeatedly. Singular systems are well-known for their applications in network analysis, biological systems, economic systems, social systems, engineering systems, time-series analysis, and many other areas of science and

In this paper, the control problem for a class of second-order sliding mode (SOSM) systems with a nonvanishing mismatched disturbance is investigated via a composite SOSM hybrid control manner. The composite SOSM hybrid control is proposed by utilizing a fixed-time disturbance observer (DOB) and a fixed-time composite SOSM controller. The fixed-time DOB is firstly developed to estimate mismatched disturbances

Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper focuses on fractional systems of order 0 < α < 1 modeled by the Atangana–Baleanu derivative of Riemann–Liouville type (ABR), which allows consistent modeling of a large class of physical systems with complex

In this work, we study some properties of weight matrices for the Dirac operator on a star graph, which are corresponding concepts to those of the Sturm-Liouville operator. There are two major ingredients. The first is devoted to the structure properties and asymptotic formulae of weight matrices. As an application, we construct a sequence of eigenfunctions and prove its Riesz basicity in the second

In this current work, we main to find the abundant explicit solutions of the Benney–Luke equation by a novel approach, which is called the variational direct method (VDM). The VDM based on the variational theory and Ritz-like method can reduce the order of the differential equation to make the equation simpler and obtain the optimal solution by the stationary conditions. The explicit solutions in terms

The multiple exp-function method and multiple rogue wave solutions method are employed for searching the multiple soliton solutions to the (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like (KP-Boussinesq-like) equation. The obtained solutions contain the first-order, second-order, third-order, and fourth-order wave solutions. At the critical point, the second-order derivative and Hessian matrix

We investigate existence and multiplicity of weak solutions for fourth-order problems involving the Leray–Lions type operators in variable exponent spaces and improve a result of Bonanno and Chinnì (2011). We use variational methods and apply a multiplicity theorem of Bonanno and Marano (2010).

In this paper, the inverse problem of initial value identification for homogeneous anomalous diffusion equation with Riemann-Liouville fractional derivative in time is studied. We prove that this kind of problem is ill-posed. We analyze the optimal error bound of the problem under the source condition and apply the quasi-boundary regularization method, fractional Landweber iterative regularization

In this paper, using the compatible theory of differential invariants, a class of exact solutions is obtained for nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs) describing rate type materials; these solutions exhibit genuine nonlinearity that leads to the formation of discontinuities such as shocks and rarefaction waves. For certain nonconstant and smooth initial

Due to the complex set of abiotic and biotic interaction variables in the ecosystems, the dynamics of animal populations are generally considered to be driven in astate-dependent manner. This paper presents an analysis of a stochastic Nicholson's blowflies model with distributed delay, which consists of the existence and uniqueness of globally positive solution, extinction, existence of positive T-periodic

In this paper, a model that was recently derived in Reinken et al. to describe the dynamics of microswimmer suspensions is studied. In particular, the global existence of weak solutions, their weak–strong uniqueness, and a connection to a different model that was proposed in Wensink et al. is shown.

This paper deals with fractional optimal control governed by semilinear equations using the increment approach. We have considered controlled object as ( Γ α s ) ( τ ) ≡ C D 0 + α s ( τ ) − B ( τ ) s ( τ ) = η ( τ , C ( τ ) ) , τ ∈ ( 0 , T ) , with the initial conditions: Γ 0 s ≡ s ( 0 ) = s 0 , Γ 1 s ≡ s ′ ( 0 ) = s 1 , where α ∈ (1, 2], s(τ) is state variable in ℝ , B(τ) ∈ Lp, ϱ(0, T), and s 0 ,

In this work, we study of the asymptotic behavior in the whole line of a thermoelastic structure with interfacial slip and second sound where the heat conduction is given by the Cattaneo law. We prove several polynomial decay estimates depending on the smoothness of initial data. The proof is based on the semigroup approach, the energy method by introducing a Lyapunov functional, and Fourier transform

We study a nonlocal wave equation with logarithmic damping, which is rather weak in the low-frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in Rn, and we study the asymptotic profile and optimal estimates of the solutions and the total energy as t → ∞ in L2 sense. In that case, some results on hypergeometric functions are useful

Design of event-triggered functional observers for linear systems subject to input and output disturbances is presented in this paper. A new dynamic event-triggered mechanism is first proposed and then a novel event-triggered interval functional observer is designed. The designed observer provides upper and lower bounds of the unknown linear function of the state vectors. By constructing a Lyapunov

This work principally probes into the stability, the existence, and control of Hopf bifurcation of new established fractional-order delayed bidirectional associative memory (BAM) neural networks with four neurons. Firstly, based on the earlier study, we set up a class of new fractional-order multiple delayed BAM neural networks with four neurons. Secondly, applying an appropriate variable transformation

We consider the regularity question of solutions for the dynamic initial-boundary value problem for the linear relaxed micromorphic model. This generalized continuum model couples a wave-type equation for the displacement with a generalized Maxwell-type wave equation for the microdistortion. Naturally, solutions are found in H1 for the displacement u and H(Curl) for the microdistortion P. Using energy

Inorganic scintillating crystals can be modelled as continua with microstructure. For rigid and isothermal crystals, the evolution of charge carriers becomes in this way described by a reaction-diffusion-drift equation coupled with the Poisson equation of electrostatic. Here, we give a survey of the available existence and asymptotic decays results for the resulting boundary value problem, the latter

The article deals with the homogeneous Stokes resolvent system in a 3D exterior domain, under inhomogeneous Dirichet boundary conditions. Solutions to this boundary value problem are estimated in Lp-norms, with the bounds in these estimates depending on the absolute value of the resolvent parameter λ in an explicit way. Two types of boundary data are considered, that is, Lp- and W2 − 1/p, p-data. It

The stability analysis of dynamic continuous structural system (DCSS) has often been investigated by discretizing it into several low-dimensional elements. The integrated results of all elements are employed to describe the whole dynamic behavior of DCSS. In this paper, DCSS is regarded as the complex dynamic network with the discretized elements as the dynamic nodes and the time-varying stiffness

In this paper, we consider the doubly critical coupled systems involving fractional Laplacian in ℝ n with partial singular weight: ( − Δ ) s u − γ 1 u | x ′ | 2 s = | u | 2 s ∗ ( β ) − 2 u | x ′ | β + η 1 2 s ∗ ( α ) | u | η 1 − 2 u | v | η 2 | x ′ | α , ( − Δ ) s v − γ 2 v | x ′ | 2 s = | v | 2 s ∗ ( β ) − 2 v | x ′ | β + η 2 2 s ∗ ( α ) | v | η 2 − 2 v | u | η 1 | x ′ | α , (0.1)where s ∈ (0, 1)

In this work, we introduce an integration matrix operator that is fully consistent with the differentiation matrix operator defined by the differential quadrature method (DQM). Using these operators, a generic differential-integral quadrature method “DIQM” is proposed to directly discretize an integro-differential equation as a system of algebraic equations. To extend the applicability of the proposed

The application of mathematics to fields such as biology, medicine, and biotechnology has resulted in quantitative relations, and mathematical biology, an interdisciplinary branch, has emerged. The considered models of cell/tissue growth are determined by cross-reaction-diffusion equations with possible transitions between malignant cells with different growth rates or healthy cells. For the considered

In this paper, we introduce the notions of equiaffine arclength and curvature with fractional order for a plane curve and compare them with the standard ones. By using these definitions, we obtain an equiaffine Frenet formula and then construct an analogue of the fundamental theorem. The plane curves of constant equiaffine curvature with fractional order are classified. Several examples are also illustrated

In this work, we present basic results and applications of Stepanov pseudo-almost periodic functions with measure. Using only the continuity assumption, we prove a new composition result of μ-pseudo-almost periodic functions in Stepanov sense. Moreover, we present different applications to semilinear differential equations and inclusions with weak regular forcing terms in Banach spaces. We prove the

In this paper, we study a fractional nonlinear Rayleigh–Stokes problem with final value condition. By means of the finite dimensional approximation, we first obtain the compactness of solution operators. Moreover, we handle the problem in weighted continuous function spaces, and then the existence result of solutions is established. Finally, because of the ill posedness of backward problem in the sense

In this study, which is the second part of quantitative analysis of total magnetic anomaly maps on archaeological sites, it is aimed to analyze the depth values of potential buried structures that cause anomalies from the total magnetic anomaly maps of an archaeological excavation area. In the first step, depth values of the structures whose boundaries were determined on the improved total magnetic

In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi-nonexpansive operators. This algorithm is constructed based on the inertial subgradient extragradient method. In addition, a strong convergence theorem for this algorithm is obtained under some extra conditions. Furthermore, an

The spread of infectious diseases is a major challenge in our contemporary world, especially after the recent outbreak of Coronavirus disease 2019 (COVID-19). The quarantine strategy is one of the important intervention measures to control the spread of an epidemic by greatly minimizing the likelihood of contact between infected and susceptible individuals. In this study, we analyze the impact of various

In this paper, we study the maximum number of limit cycles that can bifurcate from a linear center, when perturbed inside a class of planar polynomial differential systems of arbitrary degree n. Using averaging theory of first and second order, we estimate the maximum number of limit cycles that this class of systems can exhibit.

Real-world processes that display non-local behaviours or interactions, and that are subject to external impulses over non-zero periods, can potentially be modelled using non-instantaneous impulsive fractional differential equations or systems. These have been the subject of many recent papers, which rely on re-formulating fractional differential equations in terms of integral equations, in order to

In this paper we study the existence, multiplicity, and regularity of positive weak solutions for the following Kirchhoff–Choquard problem: M ∬ ℝ 2 N | u ( x ) − u ( y ) | 2 | x − y | N + 2 s d x d y ( − Δ ) s u = λ u γ + ∫ Ω | u ( y ) | 2 μ , s ∗ | x − y | μ d y | u | 2 μ , s ∗ − 2 u in Ω , u = 0 in ℝ N \ Ω , where Ω is open bounded domain of ℝ N with C2 boundary, N > 2s and s ∈ (0, 1). M models Kirchhoff-type

This paper is devoted to exploring the translation invariance and convolution invariance of doubly weighted pseudo almost automorphic stochastic processes with impulses on time scales. Based on these results, the existence and uniqueness of the doubly weighted pseudo almost automorphic solutions to a class of stochastic nonlinear impulsive equations on time scales are obtained by taking advantage of

An epidemiological model is proposed to study the transmission dynamics of the herpes virus type 2, a sexually transmitted infectious disease. This model considers two states, susceptible and infected, divides the population into sexes, assumes only heterosexual contacts and includes different transmission rates depending on whether the transmission is woman–man or man–woman. Reported and prevalence

In this study, which is the first part of quantitative analysis of total magnetic anomaly maps on archaeological sites, it is aimed to analyze the horizontal boundary values of potential buried structures that cause anomalies from the total magnetic anomaly maps of an archaeological excavation area. In the first step, the model was created in accordance with the archaeological structure. Noisy and

This special issue “Nonlinear dynamics of phase transitions” is devoted to recent trends in the mathematical description of phase transitions, which arise in many research problems ranging from physical and chemical processes to biophysics and life science. The theory of these processes and phenomena presented by leading researchers is closely connected with various areas of pure and applied mathematics

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, Riemann–Liouville nonlinear fractional boundary value problem. Under new minimal conditions on the parameters 0 ≤ s, τ ≤ 1, it is shown that, based on the upper and lower solutions method using Schauder fixed point theorem, the positive solutions in a Sobolev spaces exist

No abstract is available for this article.

Using a thermal shock of the ramp type, the authors constructed a unique mathematical three-phase-lag scheme in a compressed rotating isotropic homogeneous micropolar thermo-viscoelastic medium. The model is applied to solve an issue of an exactly performing half-space exposed to defined boundary circumstances with an electromagnetic field. Normal mode analysis and Lame's potentials methods were used

In the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro-electro-mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady-state problem is investigated estimates of the pull-in voltage are derived. In particular, a Pohožaev's

In this paper, we study the semilinear beam equation with a locally distributed nonlinear damping on a smooth bounded domain. We first construct approximate solutions, and we show that the aforementioned approximate solutions decay uniformly in the weak phase space by using an observability inequality associated to the linear problem and a unique continuation property. Then, we prove the global existence

In this paper, a procedure for the detection of the sources of industrial noise and the evaluation of their distances is introduced. The above method is based on the analysis of acoustic and optical data recorded by an acoustic camera. In order to improve the resolution of the data, interpolation and quasi interpolation algorithms for digital data processing have been used, such as the bilinear, bicubic

We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of the elementary symmetric functions of the eigenvalues splitting a multiple eigenvalue, as well as a Rellich-Nagy-type result describing the corresponding bifurcation

The foam drainage mainly depends on the influence of gravity and foam surface tension. In this work, we consider the foam drainage in a microgravity condition, and its fractal modification is established by using the fractal derivative. The variational principle of the novel fractal model is successfully obtained by the semi-inverse method. Finally, an analytical solution is obtained by the variational

We propose to couple finite element simulations and wavelet-based post-processing analysis to explore deeply the interaction degree of microscopic events on the gross behavior of complex bodies (which class includes metamaterials), above all around material or load discontinuities. After summarizing the theoretical structures our procedure refers to, as a sample case we select a special class of complex

We consider a stationary boundary value problem describing a radiative-conductive heat transfer in a system consisting of one absolutely black body and several semitransparent bodies. To describe the radiative transfer, the integro-differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on

Based on the least-squares method, we proposed a new algorithm to obtain the solution of the second kind of regular and weakly singular Volterra-Fredholm integral equations in reproducing kernel spaces. The stability and uniform convergence of the algorithm are investigated in detail. Numerical experiments verify the theoretical findings. Meanwhile, this method is also applicable to the nonlinear Volterra

We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretization, outline the implementation, and showcase numerical examples.

We study a nonlocal evolution equation generalising a model introduced by Shigeru Kondo to explain colour patterns on a skin of a guppy fish. We prove the existence of stationary solutions using either the bifurcation theory or the Schauder fixed-point theorem. We also present numerical studies of this model and show that it exhibits patterns similar to those modelled by well-known reaction-diffusion

This work is concerned with the stationary Poisson-Nernst-Planck equation with a large parameter which describes a huge number of ions occupying an electrolytic region. First, we focus on the model with a single specie of positive charges in one-dimensional bounded domains due to the assumption that these ions are transported in the same direction along a tubular-like mircodomain. We show that the

This note presents the restricted divisor functions and describes the amicable pairs and their iterations and the iterated stable numbers derived from these new functions. These arithmetic functions are related to (2)-type Mersenne primes 2p − 1, (2, 3)-type Mersenne primes 2i · 3j − 1 and multiperfect numbers. Using Mathematica 11.2, we have tabulated all iterated stable numbers and iterated amicable

The first case of COVID-19 in India detected on January 30, 2020, after its emergence in Wuhan, China, in December 2019. The lockdown was imposed as anemergency measure by the Indian government to prevent the spread of COVID-19 but gradually eased out due to its vast economic consequences. Just 15 days after the relaxation of lockdown restrictions, Delhi became India's worst city in terms of COVID-19

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of a general class of magnetic field and electric potential from boundary measurements. Assuming the knowledge of the unknown coefficients close to the boundary, we obtain other results of stable recovery with

In this manuscript, our primary focus on the approximate controllability outcomes for non-densely defined Sobolev-type Hilfer fractional neutral differential system with infinite delay. By applying the findings and facts associated with fractional theory and the fixed-point method, the principal discussions are demonstrated. First, we focus on the existence and then discuss the approximate controllability

We present a finite difference method for a system of two singularly perturbed initial-boundary value semilinear reaction–diffusion equations. The highest order derivatives are multiplied by small perturbation parameters of different magnitudes. The problem is discretized using a central difference scheme in space and backward difference scheme in time on a Shishkin mesh. The convergence analysis has

In this study, we obtained two kinds of Wirtinger type q-inequalities on quantum calculus. Then, we proved a more general Wirtinger type q-integral inequality. With all these, we obtained classical results for q → 1−.

In this research, we study analytically the double-chain model. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the deoxyribonucleic acid molecule, connected with each other by an elastic membrane (or some linear springs) representing the hydrogen bonds between the base pairs of the two chains. The new extended direct algebraic method