In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solu...In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.展开更多
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 whi...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.展开更多
In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical s...In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical solution of the model in fractional order. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results.展开更多
In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into ex...In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into exact solution. The method is described and illustrated with different examples and figures are plotted accordingly. The obtained result confirm that DTM is very easy, effective and convenient.展开更多
In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fraction...In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and N-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.展开更多
The aim of this paper is to present a numerical study of oscillatory motion of Oldroyd-B fluid in a uniform magnetic field through a small circular pipe. First, we derive the orientation stress tensor by considering t...The aim of this paper is to present a numerical study of oscillatory motion of Oldroyd-B fluid in a uniform magnetic field through a small circular pipe. First, we derive the orientation stress tensor by considering the Brownian force. Then, the orientation stress tensor is incorporated by taking Hookean dumbbells on Brownian configuration fields in the Oldroyd-B model. The Oldroyd-B model is then reformulated coupled with the momentum equation and the total stress tensor. Finally, we analyze the orientation stress tensor in the pipe by the numerical simulations of the model and showed that the effect of orientation stress tensor is considerable although the Brownian force is sufficiently small.展开更多
文摘In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.
文摘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.
文摘In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical solution of the model in fractional order. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results.
文摘In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into exact solution. The method is described and illustrated with different examples and figures are plotted accordingly. The obtained result confirm that DTM is very easy, effective and convenient.
文摘In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and N-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.
文摘The aim of this paper is to present a numerical study of oscillatory motion of Oldroyd-B fluid in a uniform magnetic field through a small circular pipe. First, we derive the orientation stress tensor by considering the Brownian force. Then, the orientation stress tensor is incorporated by taking Hookean dumbbells on Brownian configuration fields in the Oldroyd-B model. The Oldroyd-B model is then reformulated coupled with the momentum equation and the total stress tensor. Finally, we analyze the orientation stress tensor in the pipe by the numerical simulations of the model and showed that the effect of orientation stress tensor is considerable although the Brownian force is sufficiently small.
