该文考虑了一类时间变换的强马氏过程,时间变换是截断从属过程的逆过程,这是对文章(Chen Zhenqing.Time fractional equations and probabilistic representation.Chaos Solitons and Fractals,2017,102:168-174)中结论的推广.该文建立...该文考虑了一类时间变换的强马氏过程,时间变换是截断从属过程的逆过程,这是对文章(Chen Zhenqing.Time fractional equations and probabilistic representation.Chaos Solitons and Fractals,2017,102:168-174)中结论的推广.该文建立了一种从一般Bernstein函数到广义时间分数阶偏微分方程的对应关系.展开更多
Dynamic numerical simulation of water conditions is useful for reservoir management. In remote semi-arid areas, however, meteorological and hydrological time-series data needed for computation are not frequently measu...Dynamic numerical simulation of water conditions is useful for reservoir management. In remote semi-arid areas, however, meteorological and hydrological time-series data needed for computation are not frequently measured and must be obtained using other information. This paper presents a case study of data generation for the computation of thermal conditions in the Joumine Reservoir, Tunisia. Data from the Wind Finder web site and daily sunshine duration at the nearest weather stations were utilized to generate cloud cover and solar radiation data based on meteorological correlations obtained in Japan, which is located at the same latitude as Tunisia. A time series of inflow water temperature was estimated from air temperature using a numerical filter expressed as a linear second-order differential equation. A numerical simulation using a vertical 2-D （two-dimensional） turbulent flow model for a stratified water body with generated data successfully reproduced seasonal thermal conditions in the reservoir, which were monitored using a thermistor chain.展开更多
With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equatio...With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.展开更多
In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomts...In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.展开更多
On the basis of Lie group theory,(1 + N)-dimensional time-fractional partial differential equations are studied and the expression of η_α~0 is given. As applications, two special forms of nonlinear time-fractional d...On the basis of Lie group theory,(1 + N)-dimensional time-fractional partial differential equations are studied and the expression of η_α~0 is given. As applications, two special forms of nonlinear time-fractional diffusionconvection equations are investigated by Lie group analysis method. Then the equations are reduced into fractional ordinary differential equations under group transformations. Therefore, the invariant solutions and some exact solutions are obtained.展开更多
We propose a fractional time scale to model the calcium ion channels model which is retarded with injection of calcium-chelator Ethylene Glycol Tetraacetic Acid （EGTA）. By using this nonlinear time scale and Modifie...We propose a fractional time scale to model the calcium ion channels model which is retarded with injection of calcium-chelator Ethylene Glycol Tetraacetic Acid （EGTA）. By using this nonlinear time scale and Modified Riemann-Liouville fractional derivative, we convert the integer-order calcium ion channels model into fractional-order differential equations. We also analyze the range of order of fractional-order differentiM equations to ensure the equilibria of it are asymptotically stable. The simulation results are given to demonstrate the solutions of this model coincide with the real experiment data.展开更多
Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivat...Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.展开更多
文摘该文考虑了一类时间变换的强马氏过程,时间变换是截断从属过程的逆过程,这是对文章(Chen Zhenqing.Time fractional equations and probabilistic representation.Chaos Solitons and Fractals,2017,102:168-174)中结论的推广.该文建立了一种从一般Bernstein函数到广义时间分数阶偏微分方程的对应关系.
文摘Dynamic numerical simulation of water conditions is useful for reservoir management. In remote semi-arid areas, however, meteorological and hydrological time-series data needed for computation are not frequently measured and must be obtained using other information. This paper presents a case study of data generation for the computation of thermal conditions in the Joumine Reservoir, Tunisia. Data from the Wind Finder web site and daily sunshine duration at the nearest weather stations were utilized to generate cloud cover and solar radiation data based on meteorological correlations obtained in Japan, which is located at the same latitude as Tunisia. A time series of inflow water temperature was estimated from air temperature using a numerical filter expressed as a linear second-order differential equation. A numerical simulation using a vertical 2-D （two-dimensional） turbulent flow model for a stratified water body with generated data successfully reproduced seasonal thermal conditions in the reservoir, which were monitored using a thermistor chain.
基金supported by National Natural Science Foundation of China (Grant Nos.10901027 and 11171274)Foundation of Hunan Educational Committee (Grant No. 10C0370)
文摘With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.
文摘In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.
基金Supported by the Natural Science Foundation of China under Grant Nos.11371287 and 61663043
文摘On the basis of Lie group theory,(1 + N)-dimensional time-fractional partial differential equations are studied and the expression of η_α~0 is given. As applications, two special forms of nonlinear time-fractional diffusionconvection equations are investigated by Lie group analysis method. Then the equations are reduced into fractional ordinary differential equations under group transformations. Therefore, the invariant solutions and some exact solutions are obtained.
基金Acknowledgments The research of this paper is supported by National Natural Science Foundation of China （Grant No. 11171238） and a project supported by Scientific Research Fund of Sichuan Provincial Education Department （Grant No. 13ZA0109）.
文摘We propose a fractional time scale to model the calcium ion channels model which is retarded with injection of calcium-chelator Ethylene Glycol Tetraacetic Acid （EGTA）. By using this nonlinear time scale and Modified Riemann-Liouville fractional derivative, we convert the integer-order calcium ion channels model into fractional-order differential equations. We also analyze the range of order of fractional-order differentiM equations to ensure the equilibria of it are asymptotically stable. The simulation results are given to demonstrate the solutions of this model coincide with the real experiment data.
文摘Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.
