Existence and Controllability Results of Impulsive Fractional Neutral Integro-differential Equation with Sectorial Operator and Infinite Delay

In this paper, we deal with the existence, uniqueness and controllability results for fractional impulsive neutral functional integro-differential evolution equation in Banach spaces. The main techniques depend on the fractional calculus properties of characteristic solution operators and sectorial operators. Particulary, we do not consider that the system produces a compact semi-group. So we claim that phase space for infinite delay with impulse. Finally an example is given to illustrate for our required results.