tailieunhanh - Báo cáo hóa học: " Monotone iterative technique for impulsive fractional evolution equations"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Monotone iterative technique for impulsive fractional evolution equations | Mu and Li Journal of Inequalities and Applications 2011 2011 125 http content 2011 1 125 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Monotone iterative technique for impulsive fractional evolution equations Jia Mu and Yongxiang Li Correspondence mujia88@163. com Department of Mathematics Northwest Normal University Lanzhou Gansu 730000 People s Republic of China Springer Abstract In this article the well-known monotone iterative technique is extended for impulsive fractional evolution equations. Under some monotone conditions and noncompactness measure conditions of the nonlinearity some existence and uniqueness results are obtained. A generalized Gronwall inequality for fractional differential equation is also used. As an application that illustrates the abstract results an example is given. 2000 MSC 26A33 34K30 34K45. Keywords impulsive fractional evolution equations existence and uniqueness monotone iterative technique Gronwall inequality noncompactness measure 1 Introduction In this article we use the monotone iterative technique to investigate the existence and uniqueness of mild solutions of the impulsive fractional evolution equation in an ordered Banach space X Dau t Au t f t u t t e I t tk Xu t tk Ik u tk k 1 2 . m u 0 X0 e X where Da is the Caputo fractional derivative of order 0 a 1 A D A c X X is a linear closed densely defined operator - A is the infinitesimal generator of an analytic semigroup of uniformly bounded linear operators T t t 0 I 0 T T 0 0 t0 t1 t2 . tm tm 1 T f I X X X is continuous Ik X X is a given continuous function Au t tk u t u t where u t and u t represent the right and left limits of u t at t tk respectively. Fractional-order models are found to be more adequate than integer-order models in some real-world problems. Fractional derivatives describe the property of memory and heredity of materials and it is the major advantage of fractional .