Solutions For System Of Equations Research Articles

Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space

In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative of non-integer-order 1<α≤2 and the parameter 0<ρ<1 are used to establish our model. The ρ-Laplace transform and strongly continuous cosine and sine families of uniformly bounded linear operators are adapted to obtain the mild solution. The Leray–Schauder alternative theorem and Banach contraction principle are used to demonstrate the mild solution’s existence and uniqueness in abstract phase space. The results are applied to the fractional wave equation.

Existence of solutions for hybrid systems of differential equations under exogenous information with discontinuous source term

In the mathematical modeling framework, the adoption of multiscale approaches provides a better alternative to the well-known individual-based and continuum ones. From a mathematical point of view, the emerging class of systems is characterized by the coupling of ordinary and partial differential equations. Generalizing the hybrid structure of models of the literature, we prove the existence of a weak solution for the case in which discontinuous functions model the source term of the parabolic equation, and we provide also some regularity properties.

Mean Latin Hypercube Runge-Kutta Method to Solve the Influenza Model

In this study, we propose a suitable solution for a non-linear system of ordinary differential equations (ODE) of the first order with the initial value problems (IVP) that contains multi variables and multi-parameters with missing real data. To solve the mentioned system, a new modified numerical simulation method is created for the first time which is called Mean Latin Hypercube Runge-Kutta (MLHRK). This method can be obtained by combining the Runge-Kutta (RK) method with the statistical simulation procedure which is the Latin Hypercube Sampling (LHS) method. The present work is applied to the influenza epidemic model in Australia in 1919 for a previous study. The comparison between the numerical and numerical simulation results is done, discussed and tabulated. The behavior of subpopulations is shown graphically. MLHRK method can reduce the number of numerical iterations of RK, and the number of LHS simulations, thus it saves time, effort, and cost. As well as it is a faster simulation over the distribution of the LHS. The MLHRK method has been proven to be effective, reliable, and convergent to solve a wide range of linear and nonlinear problems. The proposed method can predict the future behavior of the population under study in analyzing the behavior of some epidemiological models.

МОДЕЛИРОВАНИЕ ЭЛЕКТРОПРИВОДА ПЕРЕМЕННОГО ТОКА С АЛГОРИТМАМИ ПРОСТРАНСТВЕННО-ВЕКТОРНОЙ МОДУЛЯЦИИ

The relevance of investigation of induction motor electric drives with frequency converters having voltage source inverter with space-vector modulation is shown. The brief survey of researches of such matter is carried out. The aim of this article is to develop mathematical and computer model of frequency converter with space-vector modulation algorithms by means of Matlab Simulink, this model has to be implemented into the Matlab models of AC electric drives with induction and synchronous motors. To achieve such an aim, it needs to introduce techniques of electric drive theory, numerical techniques, techniques of algebraic equations system solution, techniques of computer simulation. The still two-phase framework is applied to describe the converter model. The two-level voltage source inverter is chosen for the investigation of modulation algorithms. To verify the mathematical model of space-vector modulation, the model of 5.5 kW induction motor is used. Induction motor and power switches are modelled by means of Matlab SimPowerSystems units. The results of simulation show the adequacy of the developed model in both steady state and transient modes. One can conclude the dependence of total harmonic distortion of the induction motor stator current from load torque, switching frequency of voltage source inverter’s power switches and stator current frequency for the electric drive with scalar control system.

Model Epidemi Suspected Exposed Infected Recovered (SEIR) Pada Penyebaran COVID-19 Orde-Fraksional

This article discusses the solution to the fractional order SEIR equation with the help of the Homotopy Perturbation Method (HPM). This mathematical model is the SEIR model of the spread of COVID-19 cases in Indonesia. In general, the nonlinear Ordinary Differential Equation System (ODES) solution is quite difficult to solve analytically, so this research will transform the nonlinear ODES into a Fractional Differential Equation System (FDES). The method used in completing this research is the HPM method. The solution for the fractional order by the HPM method is obtained by the following steps: 1). Multiply each SEIR equation against the embedding parameter and equate each coefficient in the assumed infinite series to find the solution, 2). Simulate numerical solutions and perform graph interpretation. The numerical simulation shows that the susceptible human population, the infected human population without symptoms, the recovered human population has increased, in contrast to the infected human population with decreased symptoms. The HPM method in its numerical solution shows a fairly small comparison to the nonlinear ODES solution.

Application of Lie Symmetry to a Mathematical Model that Describes a Cancer Sub-Network

In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the cell cycle. The primary purpose of this paper is to apply the techniques of Lie symmetry to the model and present some approximated solutions for the three-dimensional system of first-order ordinary differential equations describing a cancer sub-network. The result shows that the phosphatase gene (Cdc25A) regulates the cyclin-dependent kinases inhibitor (P27Kip1). Furthermore, this research discovered that the activity that reverses the inhibitory effects on cell cycle progression at the R-checkpoint initiates a pathway.

The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model

In this paper, least squares homotopy perturbation is presented as a straightforward and accurate method to compute approximate analytical solutions for systems of ordinary differential equations. The method is employed to solve a problem related to a laminar flow of a viscous fluid in a semi-porous channel, which may be used to model the blood flow through a blood vessel, taking into account the effects of a magnetic field. The numerical computations show that the method is both easy to use and very accurate compared to the other methods previously used to solve the given problem.

Over Mortality and Labor Productivity Lose Attributable to Smoking

Introduction: The labor productivity lose because of smoking can be separated by final result in absolute or relative. The absolute is the one that is associated to mortality and then is irreversible because implicate the death of consumer of cigarettes or tobacco in conditions able to work according to local law. This is the labor productivity lose that focus the attention of this research. Objective: To design a procedure to determine the social cost by absolute labor productivity lose attributable to smoking. Materials and Methods: The procedure was made taking account empirical methods as the descriptive statistic, solution of equation system and differential calculus. Results: The procedure designed is appliable for transversal research only. For logitudinal research, the procedure need be applied for each time period. Nevertheless, the CIT develop might contribute with an apk to standarizate the calculus. The application of the procedure at Cuban context in 2011 showed the feasibility from their aplicability. Conclusions: Was made a procedure to estimate the social cost by absolute labor productivity lose attributable to smoking. The procedure is useful in transversal research.

Well-Posedness and Stability for a System of Klein-Gordon Equations

In this paper, we study the weak existence of solution for a non-linear hyperbolic coupled system of Klein-Gordon equations with memory and source terms using the Faedo-Galerkin method techniques and compactness results, we have demonstrated the uniqueness of the solution by using the classical technique. In addition, we show that the solution remains stable over time. The reaction of the proper Lyapunov function is the primary tool of the proof.

Numerical Study of Thermal Radiation Phenomenon and Its Influence on Amelioration of the Heat Transfer Mechanism through MHD Non-Newtonian Casson Model

The present study’s main focus is regarding the physical properties of a two-dimensional (2D) magneto-hydrodynamic boundary layer non-Newtonian Casson fluid flow that moves due to an exponentially expanding surface with a mixed convection heat transfer mechanism. In the hydrodynamic flow and heat transmission process, the combined impact of thermal radiation and magnetic field influence is explored. The internal heat generation owing to the fluid motion or a very fluid viscosity is not taken into account. The Chebyshev spectral method (CSM) is employed in this work due to its ability, accuracy, and ease of obtaining the solution for non-linear system of ordinary differential equations (ODEs). This method is an approximate method that can usually obtain the solution in a series form. The mixed convection impact is incorporated in our problem. The results are graphed to help comprehend the many physical parameters that arise in the problem. Graphical results uncover that the speed liquid stream is lessened when reinforcing both the Casson boundary and the Hartmann number, while converse attributes are applied for the Grashof number and the radiation boundary. Finally, a comparison of our current results with previously published work on several particular situations of the problem reveals that they are in excellent agreement.

Analytical and numerical studies on a moving boundary problem of non-Newtonian Bingham fluid flow in fractal porous media

Non-Darcy flow with a threshold in fractal porous media has been widely used in the development of unconventional petroleum resources such as heavy oil and tight oil. Mathematical modeling of such challenging “threshold flow” problems with strong nonlinearity has great significance in improving petroleum science and technology. Based on a fractal theory, a new non-Darcy kinematic equation with a fractal threshold pressure gradient (TPG) is mathematically deduced in order to describe the non-Darcy flow of a non-Newtonian Bingham fluid with a threshold in fractal porous media. Then mathematical modeling of planar radial non-Darcy flow in a fractal heavy oil reservoir is performed as a nonlinear moving boundary problem. In addition, a steady analytical solution method and a transient numerical solution method are developed. The analytical solution of an ordinary differential equation system for a simple steady model is derived directly, and the transient numerical solution of a partial differential equation system for an unsteady flow model is obtained based on the finite element method with good convergence. These two model solutions are validated by cross-comparisons. It is found from the calculation results that for the steady state, the extremely disturbed moving boundary and its corresponding pressure distribution are affected only by a TPG, production pressure, and a transport exponent; by contrast, for the unsteady state, the moving boundary and its corresponding pressure distribution are affected by many more factors including the fractal dimension. Furthermore, neglect of the fractal TPG and the induced moving boundary can lead to high overestimation of well productivity.

Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions

In this paper we propose an approximation method for solving second kind Volterra integral equation systems by radial basis functions. It is based on the minimization of a suitable functional in a discrete space generated by compactly supported radial basis functions of Wendland type. We prove two convergence results, and we highlight this because most recent published papers in the literature do not include any. We present some numerical examples in order to show and justify the validity of the proposed method. Our proposed technique gives an acceptable accuracy with small use of the data, resulting also in a low computational cost.

Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations

In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fractional-order in the Caputo derivative. We apply the MGMLFM and LADM on systems of nonlinear time-fractional PDEs. Precisely, we consider some important fractional-order nonlinear systems, namely Broer–Kaup (BK) and Burgers, which have found major significance because they arise in many physical applications such as shock wave, wave processes, vorticity transport, dispersal in porous media, and hydrodynamic turbulence. The analysis of these methods is implemented on the BK, Burgers systems and solutions have been offered in a simple formula. We show our results in figures and tables to demonstrate the efficiency and reliability of the used methods. Furthermore, our outcome converges rapidly to the given exact solutions.

Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow

In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Schäfer’s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.

Some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations

<abstract><p>In this paper, applying the theory of fixed points in complete gauge spaces, we establish some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations. Moreover, the paper contains an application of the theoretical results to the study of a class of systems of nonlinear ordinary differential equations.</p></abstract>

Meir-Keeler condensing operator to prove existence of solution for infinite systems of differential equations in the Banach space and numerical method to find the solution

In this paper, we establish the existence of solution for infinite systems of differential equations in the Banach sequence space n(?), ?p(1 ? p < ?) and c by using Meier-Keeler condensing operators. With the help of examples we illustrate our results in the sequence spaces. Also for validity of the results, we find an approximation of solution by using a suitable method with high accuracy.

A new tripled system of hybrid differential equations with φ-Caputo derivatives

In this paper, we study the existence of solutions for a new tripled system of hybrid differential equations with nonlocal integro multi point boundary conditions by using the φ-Caputo derivatives. The presented results are obtained by using hybrid fixed point theorems for three Dhage operators. An illustrative example is presented for the applicability of the theoretical results.

NUMERICAL SIMULATION OF WAVE PROCESSES IN PARTIALLY SATURATED POROELASTIC MEDIA (REVIEW)

The review of a number of scientific works in the field of modeling wave processes in partially saturated porous media is proposed. Review consists of three parts. In the first part of overview, classification of porous media according to the degree of saturation with a wetting filler is stated. The fundamental works of the modern theory of porous continuums, which resulted in the Biot's theory and the mixture theory, are considered. The advantages, disadvantages, as well as the conditions for the correspondence between the two approaches are indicated. The second part is devoted to scientific publications of an applied and academic nature, which are mostly devoted to the study of the features of wave processes in poroelastic media by analytical and semi-analytical methods. Special attention is paid to the works devoted to the modeling of slow longitudinal waves as a distinctive feature of wave processes in partially saturated poroelastic media. The third part gives an overview of the application of boundary element and finite element methods to study the stress-strain state of saturated and partially saturated porous media, the behavior of waves during their propagation in the media under consideration, and the analysis of local dynamic effects. The two methods are compared. Experimental works confirming theoretical results obtained within the Biot's theory are indicated. A brief analysis of modern achievements in the problems of numerical simulation of dynamic effects in semi-infinite porous media with a layered structure such as the seabed is carried out. Works on the derivation of fundamental solutions for systems of poroelasticity equations and the construction of the corresponding integral equations in time and space of the Fourier and Laplace integral transformations are considered. Works are given that consider various aspects of boundary element modeling of unsaturated porous media and the application of boundary and finite element methods on specific examples.

EXISTENCE OF SOLUTIONS FOR A COUPLED SYSTEM OF CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH <i>P</i>-LAPLACIAN OPERATOR

In this paper, by using the Schauder fixed point theorem and Banach contraction mapping principle, the existence and uniqueness of solutions for a coupled system of Caputo-Hadamard fractional differential equations with <i>p</i>-Laplacian operator are established. As applications, two examples are given to illustrate the main results. The interesting point of this article is that the boundary value conditions contain integrals, and the approximate solutions are given by using the iterative method.

Xistence Theorems for a Coupled System of Nonlinear Multi- Term Fractional Differential Equations with Nonlocal Boundary Conditions

We discuss the existence and uniqueness of solutions for a coupled system of nonlinear multi-term fractional differential equations complemented with coupled nonlocal boundary conditions by applying the methods of modern functional analysis. An example illustrating the uniqueness result is presented. Some interesting observations are also described.