In this paper, we study the traveling wave solutions of the fractional generalized reaction Duffing equation, which contains several nonlinear conformable time fractional wave equations. By the dynamic system method, ...In this paper, we study the traveling wave solutions of the fractional generalized reaction Duffing equation, which contains several nonlinear conformable time fractional wave equations. By the dynamic system method, the phase portraits of the fractional generalized reaction Duffing equation are given, and all possible exact traveling wave solutions of the equation are obtained.展开更多
In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fra...In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fractional derivatives in these equations are in the Caputo sense. We compare our numerical solutions with those numerical solutions using RK4 method. The obtained numerical results of the optimization problem model show the simplicity and the efficiency of the proposed scheme.展开更多
The ozone data observed by TOMS in every 5°N are extended into the phase space to describe the characteristics of ozone with phase trace. First of all, the fractional dimension of the ozone layer is calculated. T...The ozone data observed by TOMS in every 5°N are extended into the phase space to describe the characteristics of ozone with phase trace. First of all, the fractional dimension of the ozone layer is calculated. Then.the phase points are regarded as some discrete characteristics solution, and the parameters of mathematical model which describe the time variation of system state are retrieved, so that the nonlinear dynamic system which reflects the short-term variation of zonal average ozone layer over the tropics is rebuilt.展开更多
文摘In this paper, we study the traveling wave solutions of the fractional generalized reaction Duffing equation, which contains several nonlinear conformable time fractional wave equations. By the dynamic system method, the phase portraits of the fractional generalized reaction Duffing equation are given, and all possible exact traveling wave solutions of the equation are obtained.
文摘In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fractional derivatives in these equations are in the Caputo sense. We compare our numerical solutions with those numerical solutions using RK4 method. The obtained numerical results of the optimization problem model show the simplicity and the efficiency of the proposed scheme.
文摘The ozone data observed by TOMS in every 5°N are extended into the phase space to describe the characteristics of ozone with phase trace. First of all, the fractional dimension of the ozone layer is calculated. Then.the phase points are regarded as some discrete characteristics solution, and the parameters of mathematical model which describe the time variation of system state are retrieved, so that the nonlinear dynamic system which reflects the short-term variation of zonal average ozone layer over the tropics is rebuilt.
