Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem

The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]3 is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v3 wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v3 is spatially finite on the Riemann Sphere and the forcing is oscillatory in y3 component if the velocity v3 is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3 is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.

2023:A year of accomplishments for the 13 Science Citation Index Expanded-and Emerging Sources Citation Index-indexed Baishideng journals

In 2023,Baishideng Publishing Group(Baishideng)routinely published 47 openaccess journals,including 46 English-language journals and 1 Chinese-language journal.Our successes were accomplished through the collective dedicated efforts of Baishideng staffs,Editorial Board Members,and Peer Reviewers.Among these 47 Baishideng journals,7 are included in the Science Citation Index Expanded(SCIE)and 6 in the Emerging Sources Citation Index(ESCI).With the support of Baishideng authors,company staffs,Editorial Board Members,and Peer Reviewers,the publication work of 2023 is about to be successfully completed.This editorial summarizes the 2023 activities and accomplishments of the 13 SCIEand ESCI-indexed Baishideng journals,outlines the Baishideng publishing policy changes and additions made this year,and highlights the unique advantages of Baishideng journals.

UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS

In this article, two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.

UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N(C) WITH TRUNCATED MULTIPLICITIES

This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space p^N（C） with truncated multiplicities, and our results improve some earlier work.

Uniqueness Theorems for Meromorphic Functions of Order Less than One

In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized.

EXISTENCE, BOUNDEDNESS AND UNIQUENESS OF WEAK SOLUTION FOR THE THERMISTOR PROBLEM WITH MIXED BOUNDARV CONDITIONS

The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.

EXISTENCE AND UNIQUENESS FOR THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.

UNIQUENESS FOR SOLUTIONS OF NONHOMOGENEOUS A -HARMONIC EQUATIONS WITH VERY WEAK BOUNDARY VALUES

A uniqueness result for nonhomogeneous quasilinear elliptic partial differential equations with very weak boundary values was proved.

HOPF BIFURCATION AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF QUARTIC SYSTEM

This paper studies a class of quartic system which is more general and realistic than the quartic accompanying system.x＇=-y＋ex＋lx^2＋mxy＋ny^2,y＇=x（1-Ay）（1＋Cy^2）,（＊）where C 〉 0. Sufficient conditions are obtained for the uniqueness of limit cycle of system （＊） and some more in-depth conclusion such as Hopf bifurcation.

A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

ON THE UNIQUENESS OF BOUNDARY INTEGRAL EQUATION FOR THE EXTERIOR HELMHOLTZ PROBLEM

From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld's condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.

EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

Local Existence and Uniqueness Theorem for a Nonlinear Schrödinger Equation with Robin Inhomogeneous Boundary Condition

In recent years, a vast amount of work has been done on initial value problems for important nonlinear evolution equations like the nonlinear Schrödinger equation (NLS) and the Korteweg-de Vries equation (KdV). No comparable attention has been given to mixed initial-boundary value problems for these equations, i.e. forced nonlinear systems. But in many cases of physical interest, the mathematical model leads precisely to the forced problems. For example, the launching of solitary waves in a shallow water channel, the excitation of ion-acoustic solitons in a double plasma machine, etc. In this article, we present the PDE (Partial Differential Equation) method to study the following iut = uxx - g|u|pu, g ∈ R, p > 3, x?∈ Ω = [0,L], 0 ≤?t?u (x,0) = u0 (x) ∈?H2 (Ω) and Robin inhomogeneous boundary condition ux (0,t) + αu (0,t) = R1(t), t ≥ 0 and ux (L,t) + αu (L,t) = R2 (t), t ≥ 0 (here?α?is a real number). The equation is posed in a semi-infinite strip on a finite domain Ω. Such problems are called forced problems and have many applications in other fields like physics and chemistry. The main tool of PDE method is semi-group theory. We are able to prove local existence and uniqueness theorem for the nonlinear Schrödinger equation under initial condition and Robin inhomogeneous boundary condition.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO THE DYNAMIC EQUATIONS FOR KOITER SHELLS

In this paper, the dynamic equations for Koiter shells have been studied by Galerkin method, the existence and uniqueness to the solutions are proved.

Existence and Uniqueness of Global Smooth Solutions for Vlasov Maxwell Equations

Global existence of classical solutions to the relativistic Vlasov-Maxwell system, given sufficiently regular initial data, is a long-standing open problem. The aim of this project is to present in details the results of a paper published in 1986 by Robert Glassey and Walter Strauss. In that paper, a sufficient condition for the global existence of a smooth solution to the relativistic Vlasov-Maxwell system is derived. In the following, the resulting theorem is proved by taking initial data , . A small data global existence result is presented as well.

Existence and Uniqueness of Almost Periodic Solutions for Some Infinite Delay Integral Equations

In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.

Uniqueness of BV Entropy Solutions for Higher Dimensional Quasilinear Parabolic Equations with Arbitrary Degeneracy

We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature