In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction p...In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.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
We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their...We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.展开更多
基金supported by the NNSF of China (Grant No.11026098,11026150 and11171191)
文摘In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.
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.
文摘We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.
