Approximate controllability of impulsive fractional neutral evolution equations with Riemann-Liouville fractional derivatives
In this paper, we study the control systems of impulsive fractional neutral evolution differential equations involving Riemann-Liouville fractional derivatives in Banach spaces. Firstly, we establish the PC1-alpha-mild solution for the impulsive fractional neutral evolution differential equations. Secondly, some assumptions is made to guarantee the existence and uniqueness results of mild solutions. And under this condition, the approximate controllability of the associated impulsive fractional neutral evolution systems are formulated and proved. An example is provided to illustrate the application of the obtained theory.
approximate controllability riemann-liouville fractional derivatives pc1-alpha-mild solutions impulsive fractional evolution equations