Approximate controllability of impulsive non-local non-linear fractional dynamical systems and optimal control

Abstract

We establish existence, approximate controllability and optimal control of a class of impulsive non-local non-linear fractional dynamical systems in Banach spaces. We use fractional calculus, sectorial operators and Krasnoselskii fixed point theorems for the main results. Approximate controllability results are discussed with respect to the inhomogeneous non-linear part. Moreover, we prove existence results of optimal pairs of corresponding fractional control systems with a Bolza cost functional.2010 Mathematics Subject Classification. 26A33; 45J05; 49J15; 93B05.

Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces

“…Step II: G is a contraction on B r . For any v, w ∈ B r and 0 ≤ t ≤ T, in accordance with (12), we obtain…”

“…In the last two decades, several researchers have been interested in exploring the concept of controllability for fractional systems [11][12][13]. This is natural because fractional differential equations are considered a valuable tool in modeling various real-world dynamic systems, including physics, biology, socio-economy, chemistry and engineering [14][15][16].…”