Existence And Generalized Ulan-Hyers-Rassias Stability Of Solutions For A Class Fractional Differential Equations With Not Instantaneous Impulses

Integer order differential equation as a classical equational theory has been gerenally accepted. However, the study of complex systems and complex phenomenon often en-counter some problems. Fractional order differential equation is a generalization of the integer order differential equation, which have great advantage on dealing with relatively complex system. In view of this, in this paper, we consider the existence of solutions for a class of fractional ordinary differential equations with not instantaneous impulses, Firstly, we derive a formula of solutions for impulses fractional initial problem.Secondly, we in-troduce a concept of generalized Ulam-Hyers-Rassias stability. Moreover, we use Banach fixed point theorem, Holder inequation and Gronwall inequation to derive uniqueness and a generalized Ulam-Hyers-Rassias stability result for the impulsive fractional differential equations. Finally, an example is given to illustrate our results.