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The existence of mild solutions and approximate controllability for nonlinear fractional neutral evolution systems

Echchaffani Zoubida, Aberqi Ahmed, Karite Touria, Leiva Hugo

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 1

15--27

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.

Existence and controllability results for nonlinear differential inclusions with nonlocal conditions in Banach spaces

Benchohra M., Ntouyas S. K.

Journal of Applied Analysis

2002

Vol. 8, nr 1

33-48

In this paper we investigate the existence and controllability of mild solutions to the first order semilinear evolution inclusions in Banach spaces with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.