Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to p‐Laplace double obstacle problems involving the Schrödinger term: − Δ p u + 𝕍 | u | p − 2 u with bound constraints ψ1 ≤ u ≤ ψ2 in nonsmooth domains. This problem has its own interest in mathematics, engineering, physics, and other branches of science. Our approach makes a novel connection between the

In this study, a physical scheme called the blood liquor absorption model has been examined in its fractional (non‐integer) edict form. The constant proportional Caputo (CPC) hybrid fractional operator with singular and nonlocal kernel has been used to fractionalize the blood alcohol model. The logical solutions of the absorptions of liquor in stomach S(t) and the absorptions of liquor in the blood

Due to the non‐commutativity of quaternions, there are three kinds of quaternionic Banach spaces, i.e. the right sided, the left sided, and the two sided ones. For the left and right sided Banach spaces, the quaternion multiplications are only defined on one single side. In this paper, we characterize the quaternionic Banach spaces such that the quaternionic operator valued Fourier transforms satisfy

In a previous work, the hyperbolic conformality for bicomplex functions was introduced, and it was proved that, with the adequate hypothesis, a bicomplex holomorphic function is hyperbolic conformal. The aim of this paper is to extend this idea to 𝔻 n , with 𝔻 the set of hyperbolic numbers. Thus, the fundaments of the analysis in 𝔻 n are presented here, as well as the generalization of some geometric

We consider the Cauchy problem of the fifth‐order Korteweg–de Vries (KdV) equations without nonlinear dispersive term ∂ t u − ∂ x 5 u + b 0 u ∂ x u + b 1 ∂ x ( ∂ x u ) 2 = 0 , ( t , x ) ∈ ℝ × 𝕋 . (0.1)

The aim of this paper is to construct generating functions for a new family of polynomials, which are called parametric Hermite‐based Milne–Thomson type polynomials. Many properties of these polynomials with their generating functions are investigated. These generating functions give us generalization of some well‐known generating functions for special polynomials such as Hermite type polynomials,

In this article, the fractal‐fractional (FF) version of the fifth‐order KdV equation is introduced. The shifted Vieta‐Fibonacci (VF) polynomials are generated and adopted to establish a simple and accurate numerical method for solving this equation. To this end, the operational matrices of ordinary and FF derivatives of these polynomials are obtained in explicit forms. These matrices together with

In this paper, we investigate the size of a bidimensional fragmentation process. A rectangle of dimensions x and y is considered; it is split into four subrectangles with some probability that depends on x and y; we iterate until the stop of the process. The total number of the all the obtained rectangles at the end of the process satisfies some equality in distribution which is resolved by the contraction

The present investigation deliberates the impact of the magnetic dipole for the flow of non‐Newtonian Williamson nanoliquid by considering the thermal radiation and chemical reaction defined by the Arrhenius model. The flow model is established by incorporating the well‐known Buongiorno's nanofluid model, and as a result, Brownian motion and thermophoretic diffusion are assimilated in mathematical

In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative‐type |ut|q or the mixed‐type |u|p + |ut|q, where p, q > 1. On one hand, employing the Banach fixed‐point theorem, we prove local (in‐time) existence of mild solutions. On the other hand, under some conditions for initial data and

A reaction–diffusion system with mass conservation modeling cell polarity is considered. A range of the parameters is found where the ω‐limit set of the solution is spatially homogeneous, containing constant stationary solution as well as possible nontrivial spatially homogeneous orbit.

The main focus of this study is to investigate the impact of heat generation/absorption with single slip assumptions based on Newtonian heating on magnetohydrodynamic (MHD) time‐dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. The mathematical modeling based on fractional treatment of governing equation subject to the temperature distribution, shearing stress, and velocity

The Markov evolution is studied of an infinite age‐structured population of migrants arriving in and departing from a continuous habitat X ⊆ ℝ d —at random and independently of each other. Each population member is characterized by its age a ≥ 0 (time of presence in the population) and location x ∈ X. The population states are probability measures on the space of the corresponding marked configurations

In this paper, we consider direct problem and inverse source problem of time‐fractional Black‐Scholes type model involving hyper‐Bessel operator. Analytical solutions to these problems are constructed based on appropriate eigenfunction expansion and Erdélyi‐Kober fractional integrals whose kernel has double singularities; then, existence and uniqueness are established. At last, the results are demonstrated

One of the variants of the nonlocal Ginzburg–Landau equation is considered. This equation arises in the mathematical modeling of physical phenomena, such as ferromagnetism. For the corresponding initial boundary value problem in the case of periodic boundary conditions, current problems of the theory of infinite‐dimensional dynamical systems are considered. The question of the existence of smooth global

In this paper, we study the existence of weak solution for singular fractional Schrödinger system in ℝ N involving Trudinger–Moser nonlinearity as follows: ( − Δ ) p s u + | u | p − 2 u = H u ( x , u , v ) | x | γ ( − Δ ) p s v + | v | p − 2 v = H v ( x , u , v ) | x | γ , where N ≥ 1, 0 < s < 1, N = ps, γ ∈ [0, N), and H has exponential growth and does not satisfy the Ambrosetti–Rabinowitz condition

The main objective of the paper is to study the non‐local problem for a pseudo‐parabolic equation with fractional time and space. The derivative of time is understood in the sense of the time derivative of the Caputo fraction of the order α, 0 < α < 1. The first result is an investigation of the existence and uniformity of the solution; the formula for mild solution and the regularity properties will

The dynamics of diseases and effectiveness of control policies play important role in the prevention of epidemic diseases. To this end, this paper is concerned with the design of fractional order coronavirus disease (COVID‐19) model with Caputo Fabrizio fractional derivative operator of order Ω ∈ (0, 1] for the COVID‐19. Verify the nonnegative special solution and convergence of the scheme with in

We consider a model describing the steady flow of compressible heat‐conducting chemically reacting multicomponent mixture. We show the existence of strong solutions under the additional assumption that the mixture is sufficiently dense. We work in the Lp‐setting combining the methods for the weak solutions with the method of decomposition. The result is a generalization of previous results of the authors

The efficiency of matrix–vector multiplication is of considerable importance. No current approaches can optimize this sufficiently well under severe time constraints. All major existing methods are based on either manual‐tuning or auto‐tuning and can therefore be time‐consuming. We introduce an alternative model‐driven approach, which is used to map the implementation of matrix–vector multiplication

In this paper, we consider the regularity of weak solutions to the 3D magneto‐micropolar fluid equations. It is shown that if the velocity field or pressure belongs to some Lorentz spaces in both time and spatial directions, then the weak solutions are regular on [0, T]. In particular, we also obtain regularity criteria for the micropolar fluid equations and the MHD equations, respectively. Our results

In this paper, we consider the two‐dimensional chemotaxis‐Navier‐Stokes system with singular sensitivity n t + u · ∇ n = Δ n − χ ∇ · ( n c ∇ c ) , x ∈ Ω , t > 0 , c t + u · ∇ c = Δ c − c + n , x ∈ Ω , t > 0 , u t + κ ( u · ∇ ) u = Δ u + ∇ P + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ · u = 0 , x ∈ Ω , t > 0 in a bounded convex domain Ω ⊂ R2 with smooth boundary, with κ ∈ R and a given smooth potential ϕ : Ω → R. It

In the paper, we devote to broadening the current global regularity results for the two‐dimensional magnetic Bénard fluid equations. We study three cases: (i) fractional Laplacian dissipation (‐ Δ)αu, partial magnetic diffusion ( ∂ x 2 x 2 2 b 1 , ∂ x 1 x 1 2 b 2 ) , and Laplacian thermal diffusivity Δθ; (ii) partial fractional dissipation ( Λ x 2 2 α u 1 , Λ x 1 2 α u 2 ) , partial magnetic diffusion

The main purpose of this paper is to study a problem of recovering a parabolic equation with fractional derivative from its time averaging. This problem can be established as a new boundary value problem where a Cauchy condition is replaced by a prescribed time average of the solution. By applying some properties of the Mittag–Leffler function, we set some of the results above existence, uniqueness

The developed model of diffusion‐limited and diffusionless solidification of a eutectic alloy describes the relation “undercooling (ΔT)‐velocity (V)‐interlamellar spacing (λ)” for two cases. Namely, when the solidification front velocity V is smaller than the solute diffusion speed in bulk liquid VD, V < VD, the model predicts a regime of eutectic solidification similarly to known classical models

This article focuses on studying mild solutions of an original fractional partial differential equation disturbed by multiplicative white noise. We employ techniques of semigroup theory, Hausdorff measure, and Darbo fixed point theorem.

We conjecture that for a plasma in a spatial domain with a boundary, the specular reflection effect of the boundary can be approximated by a large magnetic confinement field in the near‐boundary region. In this paper, we verify this conjecture for the 1.5D relativistic Vlasov–Maxwell (RVM) system on a bounded domain Ω = ( 0,1 ) with an external confining magnetic field.

We investigate a class of nonlinear time‐partial differential equations describing the growth of glioma cells. The main results show sufficient conditions for the stability of stationary solutions for these kind of equations. More precisely, we study different spatial variables involving radial or axial symmetries. In addition, we also numerically simulate the system based on three distinct scenarios

In this paper, new energy functionals are described via the variational approach method. By doing this, a new class of elastic curves is described in the three‐dimensional ordinary space. An alternative method is also investigated to compute critical points of the bending energy functionals acting on a class of magnetic curves. Then, classifications of these critical curves are presented as elastic

The main aim of this study is to analyze the dynamical properties of hepatitis B‐type virus (HBV) infection in terms of mathematical model. The presented mathematical model on HBV involves the various factors such as immune impairment, total carrying capacity, logistic growth term, and antiretroviral therapies. In addition, the effect of time delays is also considered into the model, which are inevitable

This paper deals with a new multigrid method with reduced phase error for solving 2D damped Helmholtz equations. The method is obtained by taking the high‐effective, reduced phase error 5‐point finite difference (FD) scheme as a coarse grid operator and the regular 5‐point FD scheme as a fine grid operator. It is found that the proposed method gives a faster convergent rate than the regular multigrid

In this paper, we exploit the generalized bifurcation method to study space–time fractional Drinfel'd–Sokolov–Wilson equation and derive its various new exact explicit periodic wave solutions. Especially and interestingly, we find the so‐called M/W‐shaped periodic wave solutions, which were not found in previous studies. Furthermore, we uncover their inside limit relations as well as their limit relations

In this article, we consider the fourth order non‐self‐adjoint singular boundary value problem 1 r r 1 r r ϕ ′ ′ ′ ′ = ϕ ′ ϕ ″ r + λ , with λ as a parameter measures the speed at which new particles are deposited. This differential equation is non‐self‐adjoint, so finding its solutions is not easy by usual methods. Also, this does not have a unique solution; therefore, finite differences and discrete

In this paper, we define concept of the uniformly quasi circular motion (UQCM) with biharmonicity condition in the Heisenberg space. That is, we aim to define a new class of UQCM in the three‐dimensional Heisenberg space. We further improve an alternative method to find uniformly quasi circular potential electric energy of biharmonic velocity magnetic particles in the Heisenberg space. We also give

The scheme of solving the inverse problem (IP) for reconstructing three functions characterizing the radial change in the Lamé parameters and in the density in a cylindrical waveguide is presented. The displacement fields corresponding to three types of loading are used as an additional information for solving the IP. An iterative process is constructed, at each step of which a direct problem is solved

The time‐dependent slip flow and heat transport of the Cu‐Al2O3 hybrid nanofluid through a vertical permeable plate with Hall current and variable suction is investigated. An exponential heat source and quadratic convection effects are considered. The dimensionless governing equations are solved analytically using the regular perturbation method. The graph of variation of the different flow fields

This paper is concerned with a West Nile virus (WNv) model on a growing domain, which accounts for habitat expansion of mosquitoes because of climate warming. We aim to understand the relationship of the growing rate and the transmission risk of WNv. The basic reproduction number, which is related to the growing rate and diffusion rate, is introduced through spectral theory. The conditions to determine

This paper represents a system of variable‐order (VO) time fractional 2D Burgers equations and expresses a semidiscrete approach by applying the 2D Chelyshkov polynomials (CPs) for solving this system. In this model, the fractional derivative of the Caputo type is considered. To solve this system, we first discretize the VO time fractional derivatives. Next, we obtain a recurrent algorithm by using

The design of district metered areas (DMA) in potable water supply systems is of paramount importance for water utilities to properly manage their systems. Concomitant to their main objective, namely, to deliver quality water to consumers, the benefits include leakage reduction and prompt reaction in cases of natural or malicious contamination events. Given the structure of a water distribution network

The multi‐phase free convection of nano‐encapsulated phase change material (PCM)/multi‐walled carbon nanotube (MWCNT)–Fe3O4–water mixture inside an inclined porous half‐annulus collector has been simulated using the Buongiorno's mathematical model. To create the buoyancy force, the internal Corrugated and outer cylinder wall are in the high constant hot flux as the hot wall and the constant temperature

In this paper, we derive the exact analytical solution for the periodic oscillations of a nonlinear mechanical oscillator that is capable of describing phase transition phenomenon with spatially inhomogeneous distribution of the order parameter. The exact analytical solution was derived in terms of the elliptic integral of the third kind and covers the cases where the physical variable influencing

This paper presents an investigation on nonlinear forced vibration characteristics of a spinning shaft‐disk assembly resting on sliding bearing supports. Based on the Timoshenko beam theory and Kirchhoff plate theory, the coupled model of the rotor is established. The present model is validated through comparison with the experiment results for different structure parameters. Considering the gyroscopic

We consider a new approach for the numerical approximation to some classes of stochastic differential equations driven by white noise. The proposed method shares some features with the stochastic collocation techniques, and in particular, it takes advantage of the assumption of smoothness of the functional to be approximated, to achieve fast convergence. The solution to the stochastic differential

Yu‐Lan Ma, et al. (Mathematical Methods in the Applied Sciences, 2019,42(1)) make outstanding contributions for the soliton solutions of the generalized fourth‐order Boussinesq equation, which is used to describe the wave motion in fluid mechanics. But the periodic wave solution is not reported. So in this paper, He's variational methods are employed to find the solitary and periodic wave solutions

In this paper, the problem of linear functional state bounding for linear positive singular system with an interval time‐varying delay is investigated for the first time. First, the authors present new conditions for positivity, regularity, impulse free, and the existence of componentwise bound for the state vector of the singular systems without disturbance. Based on the obtained results, and by using

In the present article, free vibration behavior of carbon nanotube‐reinforced composite (CNTRC) microbeams is investigated. Carbon nanotubes (CNTs) are distributed in a polymeric matrix with four different patterns of the reinforcement. The material properties of the CNTRC microbeams are predicted by using the rule of mixture. The microstructure‐dependent governing differential equations are derived

In this paper, we analyze a modified Susceptible‐Exposed‐Infectious‐Dead‐Recovered (SEIDR) model in the literature of the Ebola disease with uncertainties. The model is constructed using a van Kampen expansion method to have an Ebola SEIDR stochastic Fokker–Planck equation model. This model has a deterministic equation and noise covariance matrix. The basic reproduction number of the deterministic

Breast cancer is a big health problem in females all over the world. It is termed as the deadliest disease in women, and the reasons of its occurrence in a human body are still unknown. In this paper, an analysis of dynamic nonlinear time‐dependent breast cancer competition model is carried out, and its numerical solution is investigated using the reliable FVIM scheme. The convergence of the solution

In the current research, we derive some existence and stability criteria for two hybrid and non‐hybrid differential equations of fractional order. By utilizing an analytical technique based on the generalized Dhage's fixed point result, we verify desired existence theorem for the hybrid problem. Also, we consider a special case as a non‐hybrid problem and by using the Kuratowski's measure of non‐compactness

In this paper, we investigate the exact solutions of a nonlinear variable coefficients time fractional biological population model using the invariant subspace method. The subspaces with dimensions one, two, and three are derived for certain cases of the variable coefficients. The exact solutions of the nonlinear time fractional biological population model are obtained in some cases.

No abstract is available for this article.

This paper investigates the analytical and semi‐analytical solutions of the time‐fractional Cahn–Allen equation, which describes the structure of dynamic for phase separation in Fe‐Cr‐X (X = Mo, Cu) ternary alloys. We apply a modified auxiliary equation method and the Adomian decomposition method to get distinct solutions to our suggested model. These solutions describe the dynamic of the phase separation

The method based on block pulse functions (BPFs) has been proposed to solve different kinds of fractional differential equations (FDEs). However, high accuracy requires considerable BPFs because they are piecewise constant and not so smooth. As a result, it increases the dimension of operational matrix and computational burden. To overcome this deficiency, a novel numerical method is developed to solve

A number of Mittag–Leffler functions are defined in the literature which have many applications across various areas of physical, biological, and applied sciences and are used in solving problems of fractional order differential, integral, and difference equations. This paper aims to define the m‐parameter Mittag–Leffler function, which can be reduced to various already known extensions of the Mittag–Leffler

In this presentation, flow physics and natural heat transfer of water/Ag nanofluid are implemented by utilizing finite volume method (FVM) considering 0–6% of solid nanoparticles in volume fraction in an elliptical‐shaped enclosure affected by different attack angles range from 45° to 135°. This survey's foremost objective is to find the optimum attack angle for the highest heat transfer performance

The paper introduces the notion of a new product summability method, which is obtained by superimposing the Zweier method on the Euler method. This method is applied to obtain the degree of approximation of Fourier series of signals (functions) belonging to certain Lipschitz classes.

The Darcy‐Forchheimer number (Fr) is dimensional.

Our aim in this paper is to study the existence and uniqueness of solutions to a Cahn‐Hilliard type model proposed for image segmentation. We also prove the existence of unbounded (as time goes to infinity) solutions and give numerical simulations which illustrate our theoretical results.

In this paper, the new exact solutions for 2D‐chiral nonlinear Schrodinger equation (CNLSE) are acquired using two proficient integration tool, namely, the new extended direct algebraic method (EDAM) and extended hyperbolic function method (EHFM). We develop soliton and some other solutions by utilizing the particular values for the parameters involved in these methods. These methods are devoted to

In this paper, we study the existence of multidimensional steady Euler–Poisson irrotational flows in general smooth bounded domains. If the conservative constant is large enough, the existence of the steady Euler–Poisson flows with low Mach number is established, provided that the normal component of current density and the tangential electric field are imposed on the boundary.