The existence of mild solutions and approximate controllability for nonlinear fractional neutral evolution systems - Echchaffani, Zoubida; Aberqi, Ahmed; Karite, Touria; Leiva, Hugo (Zielona Góra: Uniwersytet Zielonogórski)
The existence of mild solutions and approximate controllability for Reimann-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