Partial-Approximate Controllability of Nonlocal Fractional Evolution Equations via Approximating Method

TL;DR

This paper investigates the partial-approximate controllability of nonlocal fractional evolution equations using an approximating method, providing new conditions without requiring compactness or Lipschitz constraints.

Contribution

It introduces novel sufficient conditions for controllability of nonlocal fractional systems without relying on traditional compactness or Lipschitz assumptions.

Findings

Established new controllability criteria for fractional evolution equations.

Applied results to heat and delay equations.

Demonstrated effectiveness of the approximating method in control problems.

Abstract

In this paper we study partial-approximate controllability of semilinear nonlocal fractional evolution equations in Hilbert spaces. By using fractional calculus, variational approach and approximating technique, we give the approximate problem of the control system and get the compactness of approximate solution set. Then new sufficient conditions for the partial-approximate controllability of the control system are obtained when the compactness conditions or Lipschitz conditions for the nonlocal function are not required. Finally, we apply our abstract results to the parial-approximate controllability of the semilinear heat equation and delay equation.