In this paper, we introduce a novel family of multivariate neural network operators involving Riemann‐Liouville fractional integral operator of order α. Their pointwise and uniform approximation results are presented, and new results concerning the rate of convergence in terms of the modulus of continuity are estimated. Moreover, several graphical and numerical results are presented to demonstrate

Given a geometric structure on ℝ n with n = 2 m (e.g., Euclidean, symplectic, Minkowski, and pseudo‐Euclidean), we analyze the set of points inside the domain of definition of an arbitrary given C 1 vector field, where the value of the vector field equals the value of the left/right gradient–like vector field of some fixed C 2 potential function, although a natural non‐integrability condition holds

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

This work is devoted to study a class of fractional integro‐differential equations under Caputo‐Fabrizo derivative. Thank to Banach's and Krasnoselskii's fixed point theorems, the existence and uniqueness results are established for the considered problem. Further, we also derive some necessary conditions for Hyers‐Ulam and generalized Hyers‐Ulam type stability analysis to the considered problem. Finally

This paper provides a new proof of the existence and uniqueness of the solution for a nonlinear boundary value problem ( 1 + δ y ) y ′ ′ + 2 x ( 1 + γ y ) y ′ = 0 , 0 < x < ∞ , y ( 0 ) = 0 , y ( ∞ ) = 1 , which describes the study of two‐phase Stefan problems on the semi‐infinite line [0, ∞). This result considerably extends the analysis of a recent work. A highly accurate analytic approximate solution

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

Neural network has good self‐learning and adaptive capabilities. In this paper, a wavelet neural network is proposed to be used to solve the value problem of fractional differential equations (FDE). We construct a wavelet neural network (WNN) with the structure 1 ×N× 1 based on the wavelet function and give the conditions for the convergence of the given algorithm. This method uses the truncated power

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, 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

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

The engineering applications of the innovative materials, such as carbon nanotubes (CNTs) and graphene sheets, constitute a developing branch of the modern science. CNTs, in particular, exhibit extraordinarily mechanical properties capable of making them a reliable material for the above applications. The simulation of the mechanical response of a CNT is effectively conducted by a generalized beam

This paper considers the finite‐time guaranteed cost control problem for networked switched T‐S fuzzy systems. The event‐triggered scheme (ETS) and the quantization technique is employed to reduce the data transmission. T‐S fuzzy model is adopted to describe the nonlinear switched systems. Through calculation, sufficient criteria are established to verify the finite‐time boundedness of the closed‐loop

This paper is concerned with a parabolic‐elliptic Keller–Segel system where both diffusive and chemotactic coefficients (motility functions) depend on the chemical signal density. This system was originally proposed by Keller and Segel to describe the aggregation phase of Dictyostelium discoideum cells in response to the secreted chemical signal cyclic adenosine monophosphate (cAMP), but the available

This paper investigates the qualitative properties near a degenerate fixed point of a discrete predator–prey model with cooperative hunting derived from the Lotka–Volterra model where the eigenvalues of the corresponding linear operator are ±1. Applying the theory of the normal form and the Takens's theorem, we change the problem of this discrete model into the one of an ordinary differential system

A qualitative analysis for a nonlinear system of fractional pantograph evolution differential equations (FPEDEs) has been established. Conditions about the solution of the underlying equations have been established in the direction of the existence and uniqueness of the solution. Using results of fixed‐point theorems of Krasnoselskii iterations in Banach spaces, we develop the required results. This

Let L = − Δ 𝔾 + V be a Schrödinger operator on stratified Lie groups, where Δ 𝔾 is the sub‐Laplacian on 𝔾 and V belongs to the reverse Hölder class. In this paper, we introduce a new Campanato‐type space c L γ ( 𝔾 ) of vanishing mean oscillation associated with L. By Carleson measures related to fractional heat semigroups, we establish an equivalent characterization of c L γ ( 𝔾 ) . As an application

We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and extension operators over certain Sobolev spaces. Finally, we provide a weak formulation of the interior scattering problem in terms of the exterior Calderón operator

No abstract is available for this article.

The main aim of the current article is considering a nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law and deriving its approximate analytical solution in a systematic way. More precisely, after reformulating the nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law, its approximate analytical solution is derived formally through

Global existence of weak solutions to the Navier–Stokes equations coupled with the heat equation by the external force dependent on temperature is proved. The problem is considered in a cylindrical domain under boundary slip conditions and with inflow and outflow. Moreover, the Neumann boundary condition for the temperature is assumed on the lateral surface of the cylinder, while on the remaining part

In this article, a system of partial differential equations governing the one‐dimensional motion of inviscid, self‐gravitating, spherical dusty gas cloud is considered. The evolutionary behavior of spherical shock waves of arbitrary strength in an interstellar dusty gas cloud is examined. By utilizing the method based on the kinematics of the one‐dimensional motion of shock waves, we derived an infinite

Assuming non‐Fourier thermal effects, Tzou's dual‐phase‐lag model has been applied to introduce the governing heat conduction equation in the presented mathematical model. Moreover, in order to design a well‐posed dual‐phase‐lag model, the governing time fractional dual‐phase‐lag heat equation has been established by introducing conductive temperature and thermodynamical temperature, satisfying the

Full waveform seismic inversion (FWI) in the viscoelastic regime entails the task of identifying parameters in the viscoelastic wave equation from partial waveform measurements. Traditionally, one frames this nonlinear problem as an operator equation for the parameter‐to‐state map. Alternatively, in an all‐at‐once approach, one augments the nonlinear operator by the viscoelastic wave equation as an

We exploit the idea to use the maximal‐entropy method, successfully tested in information theory and statistical thermodynamics, to determine approximating function's coefficients and squared errors' weights simultaneously as output of one single problem in least‐square approximation. We provide evidence of the method's capabilities and performance through its application to representative test cases

In this paper, we pursue further analysis of the performance of a compact structure‐preserving finite difference scheme. The convergence, stability, and accuracy of the approximate solution with respect to grid refinement are discussed. The compact difference approach to precisely preserving invariants on any time‐space regions gives a three‐level linear‐implicit scheme with the spatial accuracy, found

New solutions for the elliptic Darboux equation are obtained as particular cases of solutions constructed for Heun's general equation. We consider two groups of power series expansions and two new groups of expansions in series of Gauss hypergeometric functions. The convergence of one group in power series is determined by means of ratio tests for infinite series, while the other groups are designed

The total variation model performs very well for removing noise while preserving edges. However, it gives a piecewise constant solution which often leads to the staircase effect, consequently small details such as textures are filtered out in the denoising process. Fractional‐order total variation method is one of the major approaches to overcome such drawbacks. Unlike their good quality of fractional

A mathematical model is developed for fluid flow, nutrient transport, and cell growth inside a bioreactor with a scaffold at the periphery and lumen at the centerline. The scaffold material is assumed to be deformable. In order to deal with the deformation of the solid phase and fluid phase inside the scaffold, biphasic mixture theory equations are adopted, which are derived from the theory of mixtures

The main objective of this paper is to develop a mathematical framework of pullback exponential attractors for some non‐autonomous dissipative dynamical systems via the ℓ‐trajectories methods. As an application, we prove the existence of pullback exponential attractors for three‐dimensional non‐autonomous planetary geostrophic equations of large‐scale ocean circulation, which implies that the fractal

The influences of the superheating temperature (Ts) on the nucleation undercooling (ΔT) of metallic melts were investigated by using molecular dynamics simulations based on the embedded atom model (EAM) potential function. The results agree with the intuitive expectation that extremely high heating rates followed by short equilibration time lead to a superheating and partial melting of the solid phase

In this paper, we are concerned with traveling waves in a nonlocal delayed epidemic model with diffusion. Firstly, by considering a six‐dimensional nondelayed system with the help of variable transformation, we establish the existence of monotone traveling waves by means of the abstract theory, which implies the existence of traveling waves connecting the disease‐free equilibrium and the epidemic coexistence

This article is devoted towards some necessary conditions for the existence of the mild solution of ‘second‐order semilinear stochastic delay differential equations’ having a variable delay in the state with the help of Banach fixed point theorem and theory of cosine family which is strongly continuous. In the last section, we have discussed an example to understand the theory of provided results in

A stage‐structure competition‐diffusion model with spatial heterogeneity is investigated in this paper. Under some suitable assumptions, the existence of spatially non‐homogeneous steady‐state solutions is established by investigating eigenvalue problems with indefinite weight and employing Lyapunov‐Schmidt reduction. The stability of spatially nonhomogeneous steady‐state solutions is obtained by analyzing

In this manuscript, the anti‐plane shear motion of an asymmetric three‐layered inhomogeneous elastic plate is examined. An asymptotic approach is employed for the present investigation. Both thgeneralized and unified dispersion relations within the long‐wave low‐frequency range have been successfully determined. The obtained unified dispersion relation is investigated taking into account the recently

The pivotal proposal of this work is to present a new class of harmonically convex functions, namely, generalized harmonically ψ‐convex functions based on the fractal set technique for establishing inequalities of Hermite–Hadamard type, Pachpatte type, and certain related variants with respect to the Raina's function. With the aid of an auxiliary identity correlated with Raina's function, by generalized

Accurate reporting and prediction of PM2.5 concentration is very important for improving public health. In this article, we use spectral clustering algorithm to cluster 15 cities in the Pearl River Delta. On this basis, we propose a special difference equation model, especially the use of nonlinear diffusion equations to characterize the temporal and spatial dynamic characteristics of PM2.5 propagation

This work studies a mechanical system composed of two‐spring coupled masses arrangement without damping using fractional derivatives under the Caputo sense. We determine and implement an explicit model based on the Caputo‐Fabrizio operator. To achieve this model, we detail a systematic methodology that avoids dimensional inconsistencies. Then, we use the proposed model to explain the system dynamic

In this paper, we consider two‐dimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation, the contracted mapping principle is applied. The local existence and global uniqueness results are proven. Also, the stability estimate is obtained.

We analyze the existence and uniqueness of monotone traveling wavefront for a generalized nonlinear Klein–Gordon model ∂ 2 ϕ ∂ t 2 − p + ∂ ϕ ∂ x 2 ∂ 2 ϕ ∂ x 2 + V ′ ( ϕ ) = 0 , using classical arguments of ordinary differential equations, with V(x) a potentials family containing the ϕ‐four potential V ( x ) = M 0 ( 1 − x 2 ) 2 and the sine‐Gordon‐type potential V ( x ) = ( 1 / 2 ) ( 1 + cos ( π x )

In this article, we have studied solutions of a generalised multiorder fractional partial differential equations involving the Caputo time‐fractional derivative and the Riemann–Liouville space fractional derivatives using Laplace–Fourier transform technique. Proposed generalised multiorder fractional partial differential equation is reducible to Schrödinger equation, wave equation and diffusion equation

This paper is devoted to some inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions in boundary vertices. By making use of Rouché's theorem, we derive the eigenvalue asymptotics of these operators. Besides, we show that for each of these operators, if the potentials are known a priori for all but one edge on the graph, then the potential on the remaining edge

In this paper, we study the existence and asymptotic properties of solutions to the following fractional Schrödinger equation: ( − Δ ) σ u = λ u + | u | q − 2 u + μ I α ∗ | u | p | u | p − 2 u in ℝ N under the normalized constraint ∫ ℝ N u 2 = a 2 , where N ≥ 2, σ ∈ (0, 1), α ∈ (0, N), q ∈ (2 + 4σ/N, 2N/N − 2σ], p ∈ [2, 1 + 2σ + α/N), a > 0, μ > 0, I α ( x ) = | x | α − N and λ ∈ ℝ appears as a Lagrange

This paper presents a novel model to detect the COVID‐19 infected person from a Markovian feedback persons in a limited department capacity. The persons arrive one by one to the department and the balking and the retention of reneged person approaches are considered. There exists one server presents the service to these persons according to first‐come, first‐served (FCFS) discipline. An efficient and

The continuous wavelet transform (CWT) associated with the index Whittaker transform is defined and discussed using its convolution theory. Existence theorem and reconstruction formula for CWT are obtained. Moreover, composition of CWT is discussed, and its Plancherel's and Parseval's relations are also derived. Further, the discrete version of this wavelet transform and its reconstruction formula

A computation analysis is performed to study double‐diffusive natural convection in a right‐angle trapezoidal cavity packed with a porous medium. The horizontal top and bottom boundaries are insulated and impermeable. The vertical left sidewall is kept at a constant heat flux and high concentration, whereas the inclined sidewall is held at lower temperature and concentration. The dimensionless nonlinear

The flow of electrically conducting micropolar fluid past an exponentially permeable shrinking sheet in the presence of a magnetic field and thermal radiation is studied. Similarity transformations are applied to the governing partial differential equations to form ordinary differential equations. The solution for the resultant equations, subject to boundary conditions, is then computed numerically

The current study presents a detailed analysis of two crucial real‐world problems under the Caputo fractional derivative in order to deliver some desired results for the ecosystem. In view of the fact that memory effect plays a vital role in the application, we utilize an advantageous non‐local fractional operator to investigate and analyze a mathematical model of the planktonic ecosystem and biological

In this paper, a generalized fractional (q, h)–Gronwall inequality is investigated. Based on this inequality, the uniqueness theorem and the finite–time stability criterion of nonlinear fractional delay (q, h)–difference systems are derived. Finally, several examples are given to illustrate the effectiveness of our theoretical result.

Aim of this article is to analyze the fractional order computer epidemic model. To this end, a classical computer epidemic model is extended to the fractional order model by using the Atangana–Baleanu fractional differential operator in Caputo sense. The regularity condition for the solution to the considered system is described. Existence of the solution in the Banach space is investigated and some

In this article, Haar wavelet collocation technique is adapted to acquire the approximate solution of fractional Korteweg‐de Vries (KdV), Burgers', and KdV–Burgers' equations. The fractional order derivatives involved are described using the Caputo definition. In the proposed technique, the given nonlinear fractional differential equation is discretized with the help of Haar wavelet and reduced to

This article deals with fractional model of Bratu's equation. We have solved fractional model of Bratu's equation using Chebyshev polynomials (CPs). The fractional model of Bratu's equation plays an important role in electrospinning and vibration‐electrospinning process. We have discussed the error analysis of proposed scheme. We have also provided the convergence of suggested approximate method. Numerical

This study presents a new framework to solve the coupled semilinear elliptic equation by the domain decomposition algorithm. Unlike the traditional domain decomposition algorithm, the coupled semilinear elliptic equation doesn't need to be solved directly. The strategy is to construct a set of nested finite element spaces, and subsequently solve some decoupled linear elliptic equations by using the

We extend the well‐known Halanay inequality to the fractional‐order case in presence of distributed delays and delays of neutral type (in the fractional derivative). Both the discrete and distributed neutral delays are investigated. It is proved that solutions decay toward zero in a Mittag–Leffler manner under some rather general conditions. Some large classes of kernels and examples satisfying our

In this paper, we prove a three‐ball inequality for y satisfying an equation of the form Δ 2 y = V 0 y + V 1 · ∇ y + V 2 Δ y + V 3 · ∇ Δ y in some open, connected set Ω of R n with V 0 , V 2 ∈ L ∞ ( Ω ; C ) and V 1 , V 3 ∈ L ∞ ( Ω ; C n ) . The derivation of such estimate relies on a delicate Carleman estimate for the bi‐Laplace equation and some Caccioppoli inequalities to estimate the lower‐terms

During past decades, the study of the interaction between predator and prey species has become one of the most exciting topics in computational biology and mathematical ecology. In this paper, we aim to investigate the stability of a diseased model of susceptible, infected prey and predators around an internal steady state. To this end, the fractional derivatives based on the Mittag‐Leffler kernels

In this paper, the robust stability of interval fractional order plants with one time delay controlled by fractional order controllers is investigated in a general form. For robust stability analysis of the closed loop system by the zero exclusion principle, the distance between the origin and the value set of the characteristic function needs to be checked. It is known that the outer vertices of this

The purpose of the present paper is to construct a common solution of the split null point problem associated with the maximal monotone operators and the fixed point problem associated with a finite family of k ‐demicontractive operators in Hilbert spaces. We compute the optimal common solution via inertial parallel hybrid algorithm under a suitable set of control conditions. The viability of parallel

The aim of this work is to study the stability of the reconstruction of some mechanical parameters that characterize interfaces within linear elastic bodies. The model considered consists of two bonded elastic solids. The adhesive elastic layer between them is a thin interphase that is approximated, by asymptotic analysis, as an interface. The resulting interface model is in turn characterized by a

In this paper, we consider the long‐time behavior of weak solutions for the 2D autonomous non‐Newtonian micropolar fluids. By means of the method of ℓ‐trajectories introduced by Málek and Pražák, we first establish the existence of global attractor for solution semigroup {S(t)}t ≥ 0 associated with (1)–(3) and estimate the fractal dimension of global attractor in H × L2(Ω) is finite. Then we derive

The fractional derivative with nonsingular kernel has been widely used to many physical fields which was shown to offer a new insight into the mathematical modeling of natural phenomena. In this paper, we first study the well‐posedness and regularity of the multidimensional variable‐order time‐fractional reaction–diffusion equation with Caputo–Fabrizio fractional derivative and then present and analyze