Second-Order Nonlinear Impulsive Integro-Differential Equations of Mixed Type and Optimal Controls in Fractional Power Spaces

الملخص EN

A class of second-order nonlinear impulsive integro-differential equations of mixed type whose principal part is given by time-varying generating operators in fractional power spaces is considered.

We introduce the reasonable PC-α-mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove its existence.

The existence of optimal controls for a Lagrange problem of systems governed by second-order nonlinear impulsive integro-equations of mixed type is also presented.

An example is given for demonstration.