Optimal control results for impulsive fractional delay integrodifferential equations of order 1 < r < 2 via sectorial operator

Abstract

This research investigates the existence of nonlocal impulsive fractional integrodifferential equations of order 1 < r < 2 with infinite delay. To begin with, we discuss the existence of a mild solution for the fractional derivatives by using the sectorial operators, the nonlinear alternative of the Leray–Schauder fixed point theorem, mixed Volterra–Fredholm integrodifferential types, and impulsive systems. Furthermore, we develop the optimal control results for the given system. The application of our findings is demonstrated with the help of an example.

Keywords

• fractional derivative
• infinite delay
• impulsive systems
• integrodifferential systems
• sectorial operators
• nonlocal conditions