Existence and controllability of non-local fractional dynamical systems with almost sectorial operators

Abstract

In this article, we investigate the existence of the mild solutions and controllability of nonlocal fractional dynamical system with almost sectorial operator. The dynamical system under consideration involves Caputo fractional derivative of order α∈(0,1). The existence results are proved by using fixed point theorems with suitable assumptions. Sufficient conditions for controllability are derived using appropriate control function via Leray-Schauder fixed point theorem. An example is provided to validate the results.