Graphene oxide (GO) is a mixture of carbon, oxygen, and hydrogen. GO sheets used to make tough composite materials, thin films, and membranes. GO‐water nanofluid's rheological behavior was investigated in this research. Various mass fractions: 1.0, 1.5, 2.0, 2.5, and 3.5 mg/ml; different temperature ranges: 25°C, 30°C, 35°C, 40°C, 45°C, and 50°C; and several shear ranges: 12.23, 24.46, 36.69, 61.15

The paper is devoted to the Stackelberg control of a linear parabolic equation with missing initial condition. The strategy involves two controls called follower and leader. The objective of the follower is to bring the state to a desired state while the leader has to bring the system to rest at the final time. The results are obtained by means of Fenchel–Legendre transform and appropriate Carleman

In this work, we prove some regularity criteria for a Ginzburg‐Landau‐Navier‐Stokes in superfluidity in R n ( n ≥ 3 ) .

A deterministic model for transmission of Echinococcus multilocularis (EM), a parasitic disease responsible for human alveolar echinococcosis, is formulated and analyzed rigorously. The model consists of two hosts, with three compartments each, and concentration of the parasites from environment as sources of infection. The model takes into account a predator‐prey relationship between the major hosts

In this paper, the existence of solutions is obtained for the boundary value problems to the elastic beam equations with simply supports and impulsive effects. By using the variational method and spectral structure, under the condition ( n + δ ) 4 π 4 ≤ 2 G ( t , u ) u 2 ≤ ( n + 1 − δ ) 4 π 4 ( G ( t , u ) = ∫ 0 u g ( t , s ) d s , n is a positive integer) and other conditions, we give some new criteria

We investigate the global existence and analyticity of mild solution to the three‐dimensional generalized Hall‐magnetohydrodynamics (MHD) system in this work. We prove the global existence and analyticity of solutions in the corresponding critical spaces. The work extends global existence and analyticity of solutions to Hall‐MHD system in Duan and MHD system in Wang and Ye and Zhao, to the generalized

In this paper, we consider the combined quasi‐neutral and inviscid limits of the two‐fluid compressible Navier–Stokes–Poisson system in the unbounded domain R 2 × T with the ill‐prepared initial data. We prove that the weak solutions of the compressible Navier–Stokes–Poisson system converge to the strong solution of the incompressible Euler equation as long as the latter exists. Moreover, the convergence

In the work, the psychophysical model of the signal detection theory with the nine outcomes (PMSDT9) for a quantitative description of the solution of the sensory problem of detecting an alternating differential signal was proposed. Unlike the classical model, PMSDT9 has the three probability density functions of the subjective intensity and the sign of the differential signal (instead of the two)

This paper deals with the existence and global exponential stability of almost periodic solutions for quaternion‐valued high‐order Hopfield neural networks with delays by a direct approach. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence and uniqueness of almost periodic solutions for the networks under consideration. By constructing a suitable

In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two‐dimensional multiorder time‐fractional partial differential equations: nonlinear and linear in respect to spatial and temporal variables, respectively. Fractional derivatives are estimated by Caputo sense. Boundary element method is used to convert the main problem into a system of a multiorder

We consider the inhomogeneous semilinear wave equation with linear damping ∂ttu−Δu+∂tu=|u|p+w(t,x) in ( 0 , ∞ ) × R N , where p>1 and w≢0. A general criterium for the nonexistence of global weak solutions is established. In the particular case w=ω(x), we obtain the critical exponent in the sense of Fujita (first critical exponent) and the critical exponent in the sense of Lee and Ni (second critical

In this research, the lump solution, which is rationally localized and decays along the directions of space variables, of a 2D Toda equation is studied. The effective method of constructing the lump solutions of this 2D Toda equation is derived, and the constraint conditions that make the lump solutions analytical and positive are obtained as well. Finally, three classes of lump solutions are constructed

In this paper, kinematics of semi‐real quaternionic curve in semi‐Euclidean space E 2 4 is obtained in terms of its curvature functions. The evolution equation of Frenet frame and curvatures of quaternionic curve are obtained. Also, examples of evolution equations of curvatures are given.

We revisit Cattaneo's derivation of the equation describing heat transfer and bearing his name, finding a more elaborated model equation, that we will compare with the time‐lagged model. This equation does not comply with the second law of thermodynamics, as well as Cattaneo equation. The latter, however, is known to have provided meaningful results in certain experiments conducted in some liquids

In the present paper, we introduce the notion of Cartan‐framed generalized null Mannheim curves in four‐dimensional semi‐Euclidean space with index 2, E 2 4 . We obtain the Cartan (or Frenet) frames and curvature functions of the generalized Mannheim mate curve by the help of curvature functions and Cartan frames of the generalized null Mannheim curve. We proved that there are no generalized null Mannheim

We consider some p‐Laplacian type equations with sum of nonlocal term and subcritical nonlinearities. We prove the existence of the ground states, which are positive. Because of including p=2, these results extend the results of Li, Ma and Zhang [Nonlinear Analysis: Real World Application 45(2019) 1‐25]. When p=2, N=3, by a variant variational identity and a constraint set, we can prove the existence

In this paper, we use the Galerkin weak form to construct a structure‐preserving scheme for Klein‐Gordon‐Schrödinger equation and analyze its conservative and convergent properties. We first discretize the underlying equation in space direction via a selected finite element method, and the Hamiltonian partial differential equation can be casted into Hamiltonian ordinary differential equations based

This paper is concerned with the Rayleigh–Taylor instability for the nonhomogeneous incompressible Navier–Stokes equations with Navier‐slip boundary conditions around a steady state in an infinite slab, where the Navier‐slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by Jiang et al. (Sci. China Math., 2013), we extend the result from Dirichlet boundary condition

Recently, Elfving, Hansen, and Nikazad introduced a successful nonstationary block‐column iterative method for solving linear system of equations based on flagging idea (called BCI‐F). Their numerical tests show that the column‐action method provides a basis for saving computational work using flagging technique in BCI algorithm. However, they did not present a general convergence analysis. In this

We consider the 2D hyperviscosity equations on T × R . We show that if the initial data of 2D hyperviscosity equations are ϵ‐close to the shear flows (U(y),0), which are sufficiently small perturbations of Couette flow (y,0), then the solution will stay ϵ‐close to ( e − ν t ∂ y 4 U ( y ) , 0 ) for all t>0, where ϵ ≪ ν 1 2 and ν denotes the kinematic viscosity coefficient. What is more, by the mixing‐enhanced

In this letter, two time delay dynamic models, a Time Delay Dynamical–Novel Coronavirus Pneumonia (TDD‐NCP) model and Fudan‐Chinese Center for Disease Control and Prevention (CCDC) model, are introduced to track the data of Coronavirus Disease 2019 (COVID‐19). The TDD‐NCP model was developed recently by Chengąŕs group in Fudan and Shanghai University of Finance and Economics (SUFE). The TDD‐NCP model

We study existence of a unique mild solution of evolution quantum stochastic differential equations with nonlocal conditions under the strong topology. Using the method of successive approximations, we do not need to transform the nonlocal problem to a fixed point form. The evolution operator A generates a family of semigroup that are continuous. Nonlocal conditions allow additional measurements of

In this paper, we generalize constructions of Morrey spaces by using as a basic space a general rearrangement invariant space E ( R n ) instead of L p ( R n ) and a general ideal space F ( R + ) for outer norm instead of L ∞ ( R + ) or L q , w ( R + ) . Embeddings, nontriviality conditions, and inclusion into a general concept of ideal spaces and generalized rearrangement invariant spaces are discussed

When constructing difference schemes for calculating complex problems of computational astrophysics considering magnetohydrodynamic and gravitational phenomena, the processes of matter overcompression (with a change in density by several orders of magnitude) should be taken into account, and it is important at a discrete level to take into account the corresponding energy transformations of magnetohydrodynamic

The paper deals with the existence of a global solution of a singular one‐dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized frictional damping a(x)ut using the potential well theory. Furthermore, the general decay result is proved. We construct a suitable Lyapunov functional and make use of the perturbed energy method.

This paper concerns the existence and uniqueness of the strong solutions to the initial‐boundary value problems of fractional analog of Voigt model in the planar case.

This study explores the fractional damped generalized regularized long‐wave equation in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio fractional derivatives. With the aid of fixed‐point theorem in the Atangana‐Baleanu fractional derivative with Mittag‐Leffler–type kernel, we show the existence and uniqueness of the solution to the damped generalized regularized long‐wave equation. The

A general non‐autonomous Leslie–Gower prey–predator model on time scales with control input terms is examined in the present paper. The significant property permanence is established along with the existence of almost automorphic solution of the model system. By constructing a suitable Lyapunov functional, presence of a one of a kind all‐around attractive positive almost automorphic solution of the

In this work, we investigate exact solutions of some fractional‐order differential equations arising in mathematical physics. We consider the space‐time fractional Kaup‐Kupershmidt, the space‐time fractional Fokas, and the space‐time fractional breaking soliton equations, which have important applications in science and engineering. Exact traveling wave solutions of these equations have been established

This paper analyzes the heat transfer process of nano‐encapsulated phase change material (NEPCM) particles suspended in a base fluid. NEPCMs are polyurethane‐nonadecane, and the base fluid is water. The formed suspension fills a system of two different layers: a porous layer and a clear layer. A thermally conductive solid wall transmits heat to the porous layer. These three partitions are confined

In this article, the two‐parameter Weibull model (3) is considered for microbial survival curves by new fractional differential operators to analyze some microbial, common reasons of illnesses, and outbreaks, such as Salmonella spp. cocktail in ground turkey thigh, pork shoulder, and turkey breast at isothermal cooking conditions in 50°C, 54°C, 58°C, 62°C, and 66°C, then Listeria monocytogenes and

A transmutation operator T transmuting harmonic functions into solutions of the radial Schrödinger equation S u : = △ d − q ( r ) u = 0 is studied. The potential q is assumed to be continuously differentiable, and the Schrödinger equation is considered in a star‐shaped domain Ω ⊂ R d (with d ⩾ 2 ). Several new properties of the transmutation operator are established including the operator relation

A slice theory of several octonionic variables is introduced in the article as a generalization of the holomorphic theory of several complex variables. Our new trick is to focus our attentions on some subset of O n with the same complex structures. In our setting, the Bochner‐Martinelli formula and the Hartogs extension theorems are established for slice functions of several octonionic variables.

This study is a natural continuation of modified Picard operators, defined by Agratini et al, preserving an exponential function. Herein, we first show that these operators are approximation processes in the setting of large classes of weighted spaces. Then, we obtain weighted uniform convergence of the operators via exponential weighted modulus of smoothness. Finally, we give, by using the weighted

In this work, we present conditions to obtain a global‐in‐time existence of solutions to a class of nonlinear viscous transport equations describing aggregation phenomena in biology with sufficiently small initial data in Besov‐Morrey spaces and gradient potential as a Radon measure. We also study the self‐similarity and asymptotic stability of solutions at large times.

In this paper, we are going to investigate an overdetermined problem for a general class of anisotropic equations on a cylindrical domain Ω ⊂ R N , N ≥ 2 . Our aim is to show that if the overdetermined problem admits a solution in a suitable weak sense, then the underlying domain Ω and the corresponding solution u satisfy some symmetry properties. This result represents the anisotropic extension to

In this paper, we study the time‐dependent vorticity–velocity–pressure formulation of Stokes problem in two‐ and three‐dimensional domains provided with nonstandard boundary conditions, related to the normal component of the velocity and the tangential components of the vorticity. This problem is discretized by implicit Euler's scheme in time and spectral method in space. We prove an optimal error

We propose a diffusive viral model incorporating cell‐to‐cell infection mode, nonlinear incidences, incubation period, and spatial heterogeneity. For the spatially heterogeneous model, we derive the extinction/persistence result by the basic reproduction number R 0 . For the spatially homogeneous model, we study global stabilities of steady states by establishing Lyapunov functions. The existing method

In this article, we study the near‐optimal control of a class of stochastic vegetation‐water model. The near‐optimal control is one problem in which the density of vegetation and water is higher at the lowest cost. We have provided a priori estimates of the vegetation and water densities and obtained the sufficient and necessary conditions for the system's near‐optimal control problem by applying the

In this paper, we mainly study the existence, uniqueness, and conditional stability of bounded and periodic solutions for a class of noninstantaneous impulsive linear and semilinear equations with evolution family and exponential dichotomy. We utilize the weak * convergence analysis in the conjugate space and the Banach‐Alaoglu theorem to derive the existence result, and then we use the principle of

In general, a proportional function is obviously not antiperiodic, yet a very interesting fact in this paper shows that it is possible there is an antiperiodic solution for some proportional delayed dynamical systems. We deal with the issue of antiperiodic solutions for RNNs (recurrent neural networks) incorporating multiproportional delays. Employing Lyapunov method, inequality techniques and concise

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix A . Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo‐Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in

In this article, we give some new properties of elementary operations on soft sets and then we introduce a new soft topology by using elementary operations over a universal set with a set of parameters called elementary soft topology. Also, we define a topology, members of which are collections of the soft elements and give the relation between this topology and elementary soft topology. We show that

In this paper, we establish global boundedness and Hölder regularity of the weak solution to the following parabolic p(x,t)‐Laplace equation: u t − div a ( x , t , u , ∇ u ) = b ( x , t , u , ∇ u ) in Q T , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , u ( x , 0 ) = u 0 in Ω , under some proper assumptions on a and b. The Hölder continuity given in the present work extends known results to the equation with

We apply the method of preliminary group classification to a specific class of the nonlinear heat equation, ie, u t = f ( x , u x ) u x x + g ( x , u x ) . This results in an optimal system of one‐dimensional subalgebras, which will be used to find specific forms of the equation, which admit more symmetries and so allow us to find additional group invariant solutions. We extend this work by determining

In this article, similarity reductions of the (2 + 1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order have been done by Lie group method. We have determine the geometric vector field, infinitesimal generators, symmetric groups, and commutator table of Lie algebra with the help of Lie symmetry analysis. The new close form solutions and similarity solutions of the (2 + 1)‐dimensional Bogoyavlenskii‐Schieff

The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional‐exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant

This paper deals with the 3D incompressible nematic liquid crystal flows with density‐dependent viscosity in bounded domain. The global well‐posedness of strong solutions are established in the vacuum cases, provided the assumption that ρ ¯ + ‖ ∇ d 0 ‖ L 3 is suitably small with large velocity. Furthermore, the exponential decay of the solution is also obtained.

In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann‐Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann‐Liouville fractional difference equations.

Mittag‐Leffler functions of one variable play a vital role in several areas of study. Their connections with fractional calculus enable many physical processes, such as diffusion and viscoelasticity, to be efficiently modelled. Here, we consider a Mittag‐Leffler function of two variables and the associated double integral operator, with the goal of establishing once again connections with fractional

The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one‐ and two‐dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions

In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some

The Schrödinger equation depends on the physical circumstance, which describes the state function of a quantum‐mechanical system and gives a characterization of a system evolving with time. The essential focus of proposed research is to observe the solution for fractional generalized nonlinear Schrödinger (FGNS) equation using q ‐homotopy analysis transform method ( q ‐HATM). The fractional order derivative

In this paper, we study the boundary stabilization of the deflection of a clamped‐free microbeam, which is modeled by a sixth‐order hyperbolic equation. We design a boundary feedback control, simpler than the one designed in Vatankhah et al,2 that forces the energy associated to the deflection to decay exponentially to zero as the time goes to infinity. The rate in which the energy exponentially decays

We explore the local dynamics, N‐S bifurcation, and hybrid control in a discrete‐time Lotka‐Volterra predator‐prey model in R + 2 . It is shown that ∀ parametric values, model has two boundary equilibria: P 00 ( 0 , 0 ) and P x 0 ( 1 , 0 ) , and a unique positive equilibrium point: P x y + d c , r c − d b c if c > d . We explored the local dynamics along with different topological classifications about

In this paper, a generalized nonlinear Kawahara equation with time t > 0 and x ∈ R space‐dependent coefficient is considered. We show that the construction of solution with a standard fixed point method can be accomplished so that the well‐posedness in H s ( R ) for some s > 3 / 2 is proved under a specific nonpositive differential condition. We introduce an adequate weight function to define the energy

Boundary value problems for the Euclidean Hodge‐Laplacian in three dimensions − Δ HL : = curl curl − grad div lead to variational formulations set in subspaces of H ( curl , Ω ) ∩ H ( div , Ω ) , Ω ⊂ R 3 a bounded Lipschitz domain. Via a representation formula and Calderón identities, we derive corresponding first‐kind boundary integral equations set in trace spaces of H 1 ( Ω ) , H ( curl , Ω ) ,

In this paper, we prove the existence and uniqueness of the entropy solution for a first‐order stochastic conservation law with a multiplicative source term involving a Q ‐Brownian motion. After having defined a measure‐valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure‐valued weak entropy solution

In this paper, we establish a local fractional integral identity with a parameter λ on Yang's fractal sets. Using this identity, by generalized power mean inequality and generalized Hölder inequality, two Hermite‐Hadamard type local fractional integral inequalities for generalized harmonically convex functions are established. By giving some special values to the parameter, some inequalities with specific

Two inverse problems for time‐fractional diffusion equation having a family of nonlocal boundary conditions are discussed. In first inverse problem, initial distribution is determined provided that the data at final temperature t = T is given. Second inverse problem addresses the recovery of temporal component of source term whenever total energy of the system is known. A bi‐orthogonal system of functions