<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>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.</p>
</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.

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

Laboratory of Mathematical Analysis and Applications (LAMA)

Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University

National School of Applied Sciences, Sidi Mohamed Ben Abdellah University

Laboratory of Engineering, Systems and Applications (LISA)

Department of Mathematics, School of Mathematical and Computational Sciences

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The existence of mild solutions and approximate controllability for Riemann–Liouville fractional neutral evolution systems with nonlocal conditions of a...

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

Published Online: Mar 26, 2024

Page range: 15 - 27

Received: Aug 14, 2023

Accepted: Nov 17, 2023

DOI: https://doi.org/10.61822/amcs-2024-0002

Keywords
fractional neutral evolution system, approximate controllablity, mild solution, Riemann–Liouville derivatives

© 2024 Zoubida Echchaffani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Mar 26, 2024

Page range: 15 - 27

Received: Aug 14, 2023

Accepted: Nov 17, 2023

DOI: https://doi.org/10.61822/amcs-2024-0002

Keywordsfractional neutral evolution system, approximate controllablity, mild solution, Riemann–Liouville derivatives

© 2024 Zoubida Echchaffani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fractional neutral evolution system, approximate controllablity, mild solution, Riemann–Liouville derivatives