A novel fractional case study of nonlinear dynamics via analytical approach

The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.

SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS

In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.

Exact Solutions of a Power Law Fluid Model in Posttreatment Analysis of Wire Coating with Linearly Varying Boundary Temperature

In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

The nonlinearity inmany problems occurs because of the complexity of the given physical phenomena.The present paper investigates the non-linear fractional partial differential equations’solutions using the Caputo operator with Laplace residual power seriesmethod.It is found that the present technique has a direct and simple implementation to solve the targeted problems.The comparison of the obtained solutions has been done with actual solutions to the problems.The fractional-order solutions are presented and considered to be the focal point of this research article.The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem.Because of the simple implementation,the present technique can be extended to solve other important fractional order problems.

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

In this work,We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or injection.The working of the fluid is described in the flowmodel.We can reduce the governing nonlinear partial differential equations(PDEs)to a model of coupled systems of nonlinear ordinary differential equations using similarity variables(ODEs).In order to obtain the results of a coupled system of nonlinear ODEs,we discuss a method which is known as the differential transform method(DTM).The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear ODEs.To observe beast agreement between analytical method and numerical method,we compare our result with the Rung-Kutta method of order four(RK4).We also provide simulation plots to the obtained result by using Mathematica.Onthese plots,we discuss the effect of different parameters which arise during the calculation of the flow model equations.

The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

It is eminent that partial differential equations are extensively meaningful in physics,mathematics and engineering.Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior.In the present research,mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives.First,the Helmholtz equations are presented in Caputo’s fractional derivative.Then Natural transformation,along with the decomposition method,is used to attain the series form solutions of the suggested problems.For justification of the proposed technique,it is applied to several numerical examples.The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods.The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.

Emergency Decision-Making Based on q-Rung Orthopair Fuzzy Rough Aggregation Information

With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.

求解绝对值方程的两种广义超松弛方法

绝对值方程广泛存在于运筹学、管理科学和工程领域中。对于给定的绝对值方程Ax-|x|=b,其中A为任意实矩阵,提出并分析了求解绝对值方程的广义超松弛(GSOR)方法和改进广义超松弛(MGSOR)方法.此外,研究了这两种方法的收敛性.最后,通过数值实验来验证所提方法的有效性.

Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables

In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.

Modeling and scientific computing for the transmission dynamics of Avian influenza with half-saturated incidence

This paper presents the mathematical analysis of the dynamical system for avian influenza.The proposed model considers a nonlinear dynamical model of birds and human.The half-saturated incidence rate is used for the transmission of avian influenza infection.Rigorous mathematical results are presented for the proposed models.The local and global dynamics of each model are presented and proven that when R0<1,then the disease-free equilibrium of each model is stable both locally and globally,and when R0>1,then the endemic equilibrium is stable both locally and globally.The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R0. If the basic reproduction number R0〈 1, the disease- free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R0 〉 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

Thermally stratified flow of hybrid nanofluids with radiative heat transport and slip mechanism: multiple solutions

Research on flow and heat transfer of hybrid nanofluids has gained great significance due to their efficient heat transfer capabilities.In fact,hybrid nanofluids are a novel type of fluid designed to enhance heat transfer rate and have a wide range of engineering and industrial applications.Motivated by this evolution,a theoretical analysis is performed to explore the flow and heat transport characteristics of Cu/Al_(2)O_(3) hybrid nanofluids driven by a stretching/shrinking geometry.Further,this work focuses on the physical impacts of thermal stratification as well as thermal radiation during hybrid nanofluid flow in the presence of a velocity slip mechanism.The mathematical modelling incorporates the basic conservation laws and Boussinesq approximations.This formulation gives a system of governing partial differential equations which are later reduced into ordinary differential equations via dimensionless variables.An efficient numerical solver,known as bvp4c in MATLAB,is utilized to acquire multiple(upper and lower)numerical solutions in the case of shrinking flow.The computed results are presented in the form of flow and temperature fields.The most significant findings acquired from the current study suggest that multiple solutions exist only in the case of a shrinking surface until a critical/turning point.Moreover,solutions are unavailable beyond this turning point,indicating flow separation.It is found that the fluid temperature has been impressively enhanced by a higher nanoparticle volume fraction for both solutions.On the other hand,the outcomes disclose that the wall shear stress is reduced with higher magnetic field in the case of the second solution.The simulation outcomes are in excellent agreement with earlier research,with a relative error of less than 1%.

Unsteady thin film flow of a fourth grade fluid over a vertical moving and oscillating belt

This article studies the unsteady thin film flow of a fourth grade fluid over a moving and oscillating vertical belt.The problem is modeled in terms of non-nonlinear partial differential equations with some physical conditions.Both problems of lift and drainage are studied.Two different techniques namely the adomian decomposition method(ADM)and the optimal homotopy asymptotic method(OHAM)are used for finding the analytical solutions.These solutions are compared and found in excellent agreement.For the physical analysis of the problem,graphical results are provided and discussed for various embedded flow parameters.

Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For R0〈1, the disease-free equilibrium is stable both locally and globally and for R0〉1, the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.

Control strategies of avian influenza pandemic model with time delay

A mathematical model for avian influenza with optimal control strategies is presented as a system of discrete time delay differential equations （DDEs） and its important math-ematical features are analyzed. In alignment to manage this, we develop an optimally controlled pandemic model of avian influenza and insert a time delay with exponential factor. Then we apply two controlled functions in the form of biosecurity of poultry and the education campaign against avian influenza to control the disperse of the dis- ease. Our optimal control strategies will minimize the number of contaminated humans and contaminated birds. We also derive the basic reproduction number to examine the dynamical behavior of the model and demonstrate the existence of the controlled system. For the justification of Our work, we present numerical simulations.