An investigation on the partial approximate controllability results for nonlocal neutral fractional differential systems via approximation method

Abstract

This article primarily investigates the existence and partial approximate controllability of Caputo fractional neutral differential systems with nonlocal conditions in Hilbert spaces. It employs various techniques, including fractional calculus, semigroup theory, variational approach, approximation methods, and the Schauder's fixed-point theorem. New sufficient conditions for partial approximate controllability of the control system are derived, eliminating the need for compactness or Lipschitz conditions on the nonlocal function. Additionally, an example is provided to demonstrate the obtained results.