The Existence And Uniqueness Of Two Classes Of Fractional Implusive Differential Equation

In this paper,first of all,by using the Banach's fixed-point theo-rem and Schauder's fixed-point theorem,we study the existence and uniqueness of solutions for the following fractional implusive integral-differential equation:Where J:=[0,T],t ? J':=J\{t1,t2,…,tm},CDq is the Caputo fractional derivative of order q ?(0,1).f:J × Rn × Rn ?Rn,?={(t,s):0?s?t?T},h:?×Rn? Rn.A(t)=(aij(t))(t ? J),A1,A2 are given matrices.Then,we study the existence and uniqueness of solutions for the following fractional implusive differential equation by using the Ba-nach's fixed-point theorem,Krasnoselskii's fixed-point theorem and the Leray-Schauder Nonlinear Alternative theorem.Where CD? is the Caputo fractional derivative of order ? ?(0,1),f ? C([0,1]× R?R),I?k,j and Ip are the R-L fractional integrals oforder ?k,j>0 and p ?(0,1)respectively.??R ????(p+1)/?p.