In this paper,we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations(RSFDEs)with time delay,which constitute an important class of differential equations of practical signific...In this paper,we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations(RSFDEs)with time delay,which constitute an important class of differential equations of practical significance.We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions.The numerical method is proved to be uniquely solvable,stable and convergent with second order accuracy in both space and time.Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.展开更多
In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The con...In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 〈β〈 αa 〈 1 are two parameters associated with the fractional differential equations.展开更多
In this paper,we investigate the dependence of the solutions on the parameters(order,initial function,right-hand function)of fractional delay differential equations(FDDEs)with the Caputo fractional derivative.Some res...In this paper,we investigate the dependence of the solutions on the parameters(order,initial function,right-hand function)of fractional delay differential equations(FDDEs)with the Caputo fractional derivative.Some results including an estimate of the solutions of FDDEs are given respectively.Theoretical results are verified by some numerical examples.展开更多
基金supported by National Natural Science Foundation(NSF)of China(Grant No.11501238)NSF of Guangdong Province(Grant No.2016A030313119)and NSF of Huizhou University(Grant No.hzu201806)+2 种基金supported by the startup fund from City University of Hong Kong and the Hong Kong RGC General Research Fund(projects Nos.12301420,12302919 and 12301218)supported by the NSF of China No.11971221the Shenzhen Sci-Tech Fund No.JCYJ20190809150413261,JCYJ20180307151603959,and JCYJ20170818153840322,and Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘In this paper,we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations(RSFDEs)with time delay,which constitute an important class of differential equations of practical significance.We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions.The numerical method is proved to be uniquely solvable,stable and convergent with second order accuracy in both space and time.Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.
文摘In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 〈β〈 αa 〈 1 are two parameters associated with the fractional differential equations.
基金This work is supported by the NSF of China projects(No.10971175,10871207)Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20094301110001)+1 种基金NSF of Hunan Province(No.09JJ3002,10JJ7001)the Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province of China,and NSF of Guangdong Province(No.10151601501000003).
文摘In this paper,we investigate the dependence of the solutions on the parameters(order,initial function,right-hand function)of fractional delay differential equations(FDDEs)with the Caputo fractional derivative.Some results including an estimate of the solutions of FDDEs are given respectively.Theoretical results are verified by some numerical examples.
