International Journal of applied mathematics and computer science

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Paper details

Number 1 - March 2024
Volume 34 - 2024

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

Zoubida Echchaffani, Ahmed Aberqi, Touria Karite, Hugo Leiva

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

DOI
10.61822/amcs-2024-0002