The Existence of Mild Solutions and Approximate Controllability for Nonlinear Fractional Neutral Evolution Systems

Abstract

The existence of mild solutions and approximate controllability for Riemann–Liouville fractional neutral evolution systems with nonlocal conditions of a fractional order is investigated. The Laplace transform and semigroup theory are the tools used to prove the existence. In turn, approximate controllability is proved on the basis of a Nemytskii operator, a Mittag-Leffler function and certain hypotheses using fixed point theorems, as well as the construction of a Cauchy sequence. An example is provided to highlight the main results.

Keywords

• fractional neutral evolution system
• approximate controllablity
• mild solution
• riemann–liouville derivatives